That scene also makes the contempt that many Americans had for white Confederates very apparent. To me that fact would mean that many if not most would oppose reincorporating them into the US as fellow Americans. Imagine all the stereotypes about Southerners OTL plus the actual fact that most of them were either complicit or direct participants with mass murder- Canadians,Mormons even Mexicans would be viewed as potential Americans ahead of white Confederates....
Well, I think it would be a generational thing. The US would probably institute policies which would force a 'Yankee' educational system on the children of Confederate citizens, but the Confederacy was independent for 70 years. That kind of ingrained nationalism would take decades to break down, to say nothing about Saul Goldman's wartime propaganda.