I don't think it would have any more effect of Brewster's decision than old school shows of support like cards, letters, calls or signs, but the thing about twitter is that theoretically you could show your admiration for a coach early enough in the process that he'd know that the fans really support him. And the school could see that the fans really support him.
I don't know that it would affect my employment related decision making, but it make it a little harder to leave a place if you know in advance how much you are appreciated by your customers, for lack of a better work, and your boss knows in advance too.