Even if the Whites win, then some stuff is let loose they cannot ignore or set aside. Not just the Bolshevik Revolution, but the February one happened ITTL. No one will be able to simply wind back the clock. The Civil War, curtailed as it is ITTL has also set loose some demons. I do not agree with the scenario of three generals dividing Russia as warlords, given who these men were. I can see some studiously ignoring the existence of others, for as long as they can, but Wrangel is not The Guy. He's the guy you get when all other guys walked away from the job, or were killed, but even then he is not the guy. Denikin is a bit stronger, but he's also not The Man. Yudenich is lovely in the foothills of the Caucasus, but he's not a Chinese warlord and he does not think like one. And Kolchak in death gained a reverence and a reputation he did not have within his lifetime. Just because you stuck around Chicago during Prohibition did not mean you could make it as Capone.
But back to what does the post-Bolshevik 1920s Russian state looks like, with White generals hanging about. First, everyone has just been taught might makes right. Yezhov, Stalin's other twisted goblin torturer, was a worker in the Putilov factory when the Revolution came, and the first major act he witnessed of said happening was when management were hanged from the factory gates. It taught him a valuable lesson about what state he was helping to bring about. The bleeding remains of the Russian Empire has just went through the agony of at least one year of civil war (1918 scenario), following four years of the Great War. Mass casualties are the new normal. Destruction of 300 years Imperial House, a historical fact. Hostage taking and revenge killings, a management technique. Pogroms, how we let the lads in the South get some anger out of their system. And in the end rule came to the Russian state not via a constitution and lads in three-piece suits with tails and painfully earnest faces but via bayonets, sabers, and the Cossack whip. Before United States came into being, it was a colonial extension of a nation with centuries of parliamentary tradition. Russia just had a dozen years of the Duma, interrupted by the whims of an awkward tsar, a revolution, and an armed uprising. This is not ending with a parliamentary democracy or a constitutional monarchy. You're getting Caesar, Napoleon, or a confused dictatorship by a committee.
Also, the Great War has made an utter idiot out of anyone in a position of any national authority in Russia. All those pro-War voices look like fools. All those talking a short-war, fools again. All those says it will end with a victory, damned fools. Think Italy. Russia is not emerging from the Great War happy and free, it's crawling out from the wreckage, with broken bones, shattered front teeth, and a missing a limb. Monarchism means nothing, for the Tsar had been painted by the brush of failure of the war and the subsequent chaos. Political parties who were running about prior to the Great War and were for the War, mean even less. There is no consensus, only pain and misery. And there is no coherent ideology either. The anti-Bolsheviks won, yes, but anti-Bolshevism is an umbrella term. The rain is gone. Now what? What do these winners of the Russian Civil Wars stand for exactly? The confused reforms of Wrangel? The garbled screeds of Kolchak? Yudenich's mustache? Socialism is a dirty, dirty word, associated with Bolshevism, as are the Social Democrats. But on the right, there is still chaos.
What exactly will the new Caesar offer to the masses and the officer corps? Meandering paean to exceptionalism, nationalist and chauvinism? It may tide over, as would the traditional blaming of the Jews, but then what? The land is sick, the farms are aflame, the land owners are terrified of their peasants, the harvests are meager, the corpses of factory managers hang from their gates, adn the cities are boiling with rage of a revolution suppressed. What can these four fellas with gold braid do exactly? Try to keep a lid? Muddle on? How long until it all collapses once more? Bolshevism offered a dynamic, simple, and easy to grasp ideology to the masses. As did monarchism, but the House of Romanov is destroyed, and even if a senior Romanov is dusted off and presented with a plastered over orb, it will require everyone to squint their eyes really, really hard to pretend all is at once was. Napoleon did not make himself the King of France, recall. He made himself Consul and then Emperor. New titles for new times. The Tsar is not going to cut it. So what will Russia get then, along with the new Caesar? Some sort of proto-fascist Vozhd, perhaps? A dumb new name plastered on aforementioned paean to exceptionalism, nationalist and chauvinism, maybe? But it will not be easy. The Spirit of 1917 is out there. More then a few mansions will go up a fire in the night. More than a few battleships will sink to the bottom. More than a few generals will be found floating face down in the fountains. It will take a long time. Old Bolsheviks, before Stalin rid himself of them, would routinely walk about with revolvers, long after the Russian Civil War. Memories of chaos die hard.
As to the rest of the Europe and the world at large, it depends on when this goes - 1918 vs. 1919 would change a lot, and I see others put out good scenarios on it.