One thing to realize is that for MSTP there seems to be a pronounced threshold effect with MCAT scores. As long as they are good enough, then that hurdle no longer matter, and they move on to your research. As for what "good enough" means, that varies by school, but in general mid-30's have little problem, I have a friend at Stanford who had a 33, etc., etc. If that is what you mean by average, then don't worry. If you mean a little lower than that, then I'm sure there are programs that you'll fit right into, as well.
As has been said, give it a shot, and be sure to concentrate on really knowing your stuff when it comes to research.