Judging by Fudge and Umbridge's demeanor, the voters might put more weight on the words of the Boy Who Lived than on those of Dumbledore, especially as Dumbledore wasn't phrasing his arguments in such a way as to appeal to the parts of the audience who didn't already support him.

I agree with your point about it making a poor climax though. I think it's quite unlikely for this reason, but still like the idea of Harry suddenly gaining super-lawyer powers :).