Let's say that the Confederacy successfully secceeded from USA. Is it likely that the CSA and USA would reunite at later date?
That would depend on how the two nations developed culturally and socially and politically after secession. BTW I think the CSA's main realistic shot at surviving at all is if the Union government decides to let them go without a war in the first place--and in that case, the border states will join the CSA too--if the Union is not willing to fight for the many reasons it was OTL, why struggle to retain Maryland, Delaware, and Kentucky with all of them so committed to slavery? Missouri is another matter--less overall per capita commitment to slavery for one thing, but mainly that letting MO go from the remnant Union would leave a nasty logistical hole in the map impeding access to the West. The flip side of the CSA being allowed to go in peace is that the Union will assert its control over the western territories. No, I don't think they'd concede "Oklahoma" either; not that it was called that then, it was Indian Territory. I think the Native peoples would use the split to bargain for a better deal and ultimately get one from the Union; real autonomy, their interests and rights under treaty much better respected, a seat at the table of Federal government, and more extensive reservation territory more suited to their initial locations and under better control by them. In return for this, I think if not right away then over time, the Native tribes will be quite loyal US citizens and effective and renowned as soldiers for the Army. Their more extensive reservation holdings will impede and limit western settlement somewhat, but they will permit some Anglo settlers--under their political supervision, with the tribe having the last word in these matters--in their own territories, develop cities including industrial ones, with a mix of Native and Anglo workers and owners of firms, and overall the development of the West will in aggregate be comparable to OTL, with a lot of it in Native hands. Some tribes will remain very poor, others will be richer. The Indian Territory that became Oklahoma OTL will remain first of the reservation regions, and partitioned up tribe by tribe remain Indian Territory, along with other zones.
I don't forget that some tribes had slaveholding. I suspect they will be able to retain the right to hold slaves, but it would be discouraged and it would be practical not long after the dust settles to offer compensation for emancipation--doing that on the scale of the whole South would be economically impossible, but not just for the small number the tribe members might be holding.
This fact, of Native slaveholding, is the main leverage the CSA would have in scheming to bring in Indian Territory to their side...that, and the fact that a lot of the tribes had native lands east of the Mississippi in the South that conceivably the CSA might offer restoration of as an incentive. But the secessionists were arch racists--I realize there is a distinction between different forms of racism. I notice it is a trope that in a CSA survives scenario, the Indians like the CSA better, but I don't think that has been thought out very carefully, just one of a number of shoot from the hip assumptions from glib and shallow readings of history.
So--the purpose of secession was mainly to protect the institution of slavery, and fire eater secessionists went beyond mere preservation, they were quite keen on the peculiar institution. That being the case, I anticipate some pretty hellish aspects of CSA society and for its leaders to double down, not moderate, over time. Meanwhile a cynical view would have the Union also quite bigoted, northern style--a matter of apartheid there, with "white" populations seeking to avoid any "contamination" by African American presence on any terms. But on the other hand, a certain number of freedmen of various categories (including people who remained legally fugitive slaves) were more or less tolerated, even accepted and sometimes respected, as citizens in quite a few northern communities too. Continuing to accept escaped slaves as refugees and not agreeing to remand them back to CSA custody would be a political flashpoint and some in the North would favor complying with Confederate wishes, and even deporting currently settled African Americans, if not straight into the custody of Confederate slavers than perhaps giving them a deadline before being rounded up for that purpose to make their own exits, to Canada or Liberia or wherever they could get to. Gaming out just how this dynamic develops will have great bearing on the question of whether some future reunification is possible or not, and on what terms. Certainly the Union leaders deciding to let the secessionists take their marbles (along with a certain amount looted from Federal assets) and go home would tend to defuse the saliency of slavery as an issue in the minds of many people who didn't want to be bothered; they'd figure it was no longer their problem. But it would not really go away, fugitive slaves will continue to make their way north unless the Union takes a very hard line against them. And whatever her leadership decides is expedient, the Union owes the Confederacy nothing in the way of obligations to return such fugitives to their purported owners, even if Union law continues to sanction some slave ownership by some people, such as perhaps the Native tribes (on the grounds that they are not really citizens but a subjugated foreign people with enumerated treaty relations, so able to have their own sovereignty in these questions, probably). Note I think the dynamic of the diplomatic incentive to improve relations with the Native peoples will lead to a movement toward their gaining citizenship under the USA with special rights, perhaps I can even stick in my oar for a pet idea of mine, the notion of a virtual Indian "state" which is a confederation of all tribes collectively gaining a right to House members on the basis of net population equal to states, and two Senators for the Senate, and Presidential electoral votes on this basis; the Indian Confederation not being a contiguous reservation but rather a legal grant of all Native reservations throughout the country coming under its authority, and being delegated to itself its own form of internal government which I suppose would be quilt of various tribes of very disparate sizes and backgrounds, each holding its own claims to specific reservations which collectively make up the territory of the IC.
If the Union takes a path of progressive liberalism, with robust Federal as well as encouragement of strong state democratically regulated capitalism and a pervasively liberal ideology of individual rights, of moving away from racism, eventually embracing female suffrage, and vigorous populist politics in a setting with strong professional classes and a reasonable ad hoc centralization of Federal power while retaining the states as important semiautonomous units, then culturally it will be incompatible with the most likely trajectory of the South. Attempting to incorporate CSA territory will involve a severe cultural clash and might be deemed a poison pill by Unionists. Assuming the two nations do not enter into frequent or severe military clashes, over time the idea that the two nations are properly separated will solidify into two national identities and the notion of annexing CSA territory will range from problematic to downright bizarre and even obscene. Nor will secessionist culture give much grounds for them to try to annex territory from the north...the west is another matter but I think the Union can and will stand firm there; New Mexico and on west remain Union soil. (Some Southerners might emigrate to the Union and be naturalized, and some Northerners might filter down south to take up slaveholding there, rather more of the former than the latter I would imagine, especially if the Union develops a liberal culture that frowns on slaveholding; a northerner moving to the CSA at all, especially one who proposes to buy slaves, would become persona non grata in many if not all Northern families; some states, and eventually perhaps the federal Union, would perhaps take measures to penalize such behavior by asset seizures and so forth).
However if such a liberal/reactionary divide developed, but the South later proved a major existential threat by for instance joining a military alliance against the Union and honoring their role in it by attacking, depending on the scale of the threat, if it is severe enough that the Union is fighting for its life, then the option of using the southern slaves (even if their status has evolved somewhat; it is unlikely they would be accepted as full social equals no matter what!) as subversives and insurgents to multiply Northern military strength will become attractive and once committed to African American liberation, the Union is likely to have to honor the commitment by guaranteeing the freedmen their rights and interests. This means a massive and sweeping overturn of Southern "white" society of course. Depending on how the CSA has evolved, the entire "white" majority might prove sullenly difficult to integrate, or dangerously strengthen reactionary elements in the North; it might, as southern "whites" of the OTL 1860s were, prove heterogenous, with some populations interested in autonomy on terms not too incompatibile with Union norms, others might prove actively progressive, leaving only a remnant--maybe large, maybe small--bitterly opposed to Union norms. It might work to seize only some territories and let the rest maintain CSA independence, but the slaves would have the right to walk away to Union protection and form their own autonomous states, various "white" groups might also break loose and resettle on Union provided territories, leaving a rump CSA.
If the Union has to conquer all of the South this will mean the war would be quite disruptive especially to Southern society across the whole former territory of CSA. I think Union leaders will strive to all they honorably can to avoid this. But if it happens Northern authorities will then have no qualms about imposing sweeping Reconstruction, definitely regarding seized territory as fresh conquests.
Even if the North does not develop as I hope, and racism takes some of these options off the table, on the whole I think the two societies will diverge, and fast. For one to seize territory to the other is either to swallow people on other sides of the ideological divide into each society's systems. Thus sensible politicians will give up notions of an amicable remarriage, and would be conquerors would have to face the idea, with whatever degree of disgust or enthusiasm it brings them, of massive reconstruction of conquered territory.