You would be pretty dedicated to do that. However, most people would think you are crazy. Its not like there isn't a very good program right in your own backyard.
I know of people that traveled from Houston and San Fran to Chicago.
Why would you go to Chicago over Stern? Is it a slight ranking advantage? Trust me, its not worth your extra time. I commuted over 40k miles to finish my MBA from Stern. I would not have done that for Chicago if Stern was in my backyard. Any perceived advantage would not be worth the extra time or money.