Since leaving Chicago I have lived near DC and Cincinnati, and I do root for those teams, though the Sox are still far and away my favorite team. It's easier though since those teams are NL teams. I don't think I'd root for another AL team, and definitely not another AL Central team.
I think one of the reasons the Cubs get the majority of the transplant fans is that a lot of them are coming to Chicago from other AL Central areas, especially Michigan, so they adopt the Cubs as their favorite Chicago team since it doesn't conflict with their home team.