Now, while I certainly understand that the conflict portrayed in the Turtledove series of novels was much longer, much more brutal, and much more contentious than the won that occurred IRL, I don't think that the Southern State would have turned into a version of Northern Ireland or anything like that. I would predict that a longer, more painful period of Reconstruction would have taken place instead.
This the only scenario where Reconstruction would succeed lol. In our timeline, the public grew tired of Reconstruction due to simply wanting to move on to other things, since the Confederacy was just an "insurrection" state that was barely a country. Now, after being drenched in wars and learning of Confederate genocide against negros, the public may be slightly more dedicated to a radical Reconstruction (or Reintegration) as it would prevent the possibility of the South rising again.