I'm not sure about the correlation, but there are quite a few people at Baylor who did the Baylor MMEP program. They don't guarantee you an interview or anything, but it is a good opportunity for you to make inroads and connections. You definitely have to make that effort yourself, though. Nothing is a given. You do, however, have coursework at both Rice and Baylor that are for real credit. I'm sure if you do well, that can't do anything but help you.
Best wishes,