I'm not sure things would go as we hope. I remember a debate quite a few years ago between Amy Goodman (of Democracy Now!) and a right-wing shit bag radio host (can't remember his name). Can't recall who the moderator was, if there even was one, it might actually have been an interview, but she got trashed. I support most of her positions, and where I disagree with her, that's because she's not far left enough, but you can't have a rational discussion with someone whose deep belief in his own ideology and intimate conviction that he his right allows him to lie. Revealing those lies after the fact don't change the bad impression left during the debate.
On a similar note, the debate between Ken Hammond and Bill Nye comes to mind. I don't think anyone changed their views based on that debate.