Hi jallenmorris
I know a few people who moved to Chicago just to attend school. But then I think they were able to convince their companies to transfer their positions to Chicago. I don't think you will have access to career services/ alumni before you actually start classes though.
My advice would be to just go ahead and apply to Kellogg and Chicago and maybe other schools like Stern and Haas. If you apply to start in Summer/Fall, you will have a good few months to look for a job. In the worst case, you will still have an admit and can push the start date by a quarter if you are not ready to move.
I would also let the school know your situation at the time of interviewing.I applied to Chicago and Kellogg and in both cases, I felt that the schools will help you if they can.
I would also look into Chicago's weekend program. I know that Chicago is extremely flexible with regards to classes students take( there are no restrictions with regards to what classes a student takes- a part-timer can take FT classes, weekend classes and vice versa). One possibility would be to start there on weekends and then move to Chicago once you have secured a job in the area and then take evening classes. The commute might be painful for a while but hopefully you can find a great job in area soon.
Thanks!