I don't think it would be as much of a shock as you might think. Most upstate New Yorkers are a lot more like southerners in attitude and opinion than the City folk who are like from another planet. I know I easily and happily adjusted to the South and I was raised only a county over.
If they can make the unions stay behind, most who move will be just fine and fit in. The unions have killed New York industry and jobs by the hundreds of thousands and a lot of the people know it but can't do anything about it because of who runs the State (the Liberals and unions).
You are quite right. Plenty of New Yorkers got there before them and will help make them feel welcome. It won't be necessary, however, they will be made to feel welcome by most everyone. They will probably like the fact that the city is growing, businesses, jobs, homes, etc. They will have to make a choice: be an Alabama or an Auburn fan, but you can go either way. Most importantly, when it comes time to retire, they won't have to move to the South. They'll already be there.