I don't believe so- but I'm not 100% sure. You can request to move, though and in sprin 2009 the moving fee was 50 bucks. I'm not a big drinker at all and all my roommates were. Among other thngs it was just a bad situation to live in for me so I actually moved IN to a dry apartment even though I was over 21. I just had to sign a waiver saying I wouldn't drink in the apartment.
They won't move you automatically when you turn 21, you have to request it. If you want to move to a non wellness, just tell them and they will move you. It's free too for people who turn 21 down there and want to move from wellness to non wellness.
If you decide to not move from wellness to non-wellness, you can still get a new ID after your birthday. Before your birthday, your ID will say "Under 21" on it. You can get a new one without that on it. If you don't want to move, you'll have to sign a form saying that you agree to not bring any alcohol into the apartment.