Yes and no.
I go to Wellesley. Our testing site ranked #1 in the country in Kaplan's latest post-test questionnaires--small site of 60, large real tables for each student, absolute silence--nice stuff. Wellesley students thought hey, it'd be gosh-darn convenient to take the MCAT five minutes away from our dorms at such a spiffy site. We (the 15 or so from the college taking the test) registered on the opening day to make sure. Only two of us received our first pick. I ended up spending the night in Boston to take it at my #3 testing choice.
Thus I have no idea how it works. I'm guessing that statistically, you're more likely to get your top site if you do it early. But if it's a small site, you may just have to cross your fingers.