Well, that's part of the reason that I stipulated the audience must be large enough. When you measure the audience reaction to the question before the debate, you are essentially measuring the overall bias of the room. Not everyone, but a significant enough number, is really susceptible to rational argument, logic and reason.
I don't think this is consistently the case, though. In my view, humans are not primarily rational actors. We evolved to survive, not just think rationally, and some of our heuristics, thinking patterns, and inclinations are quite prone to errors of reasoning and emotional bias.
There's also the question of which culture the audience is mainly from, since different cultures are generally more receptive to some ideas and less receptive to others. Cultural biases tend to heavily color most people's perceptions of other viewpoints, and an argument against Hinduism in India would be a lot less likely to gain traction than an argument for Islam in Iran or Saudi Arabia or one against Christianity in any of the three countries.
I can't think of any scenario where the audience could realistically be controlled for all of the cultural, personal, and emotional variables that could influence their likelihood of accepting one viewpoint or rejecting another for reasons that are not primarily or entirely based on sound logic and evidence.
Thus, if one side or the other can overcome the original bias of part of the audience, we can make a reasonable presumption that they did so using their arguments, for the simple reason that most of us don't change our minds easily.
Let me propose an example -- to simplistic but it may serve as instructive. Let's take a debate about "the existence of the Abrahamic God." Let's also assume that this is at a university, somewhere in America. The audience, being mostly students and faculty we can assume, will certainly know on which side they stand before the debate begins. A passionate speaker on the Yea side (for the existence of God), is unlikely to convince atheists with emotion. But what if he actually found an argument that could convince a few (look no further than the many such debates right here on RF)? Same thing, the Nay side atheist is really unlikely, no matter how passionate his exposition, to convince a believer to give up their belief -- unless she found some really convincing argument. It's for that reason that I suggested that the "winning side" would probably win by quite a small margin.
I think an audience at a university would still have their biases and other variables affecting their perceptions such that those variables could end up favoring one viewpoint over another, even if by a small margin, due to factors that may not be primarily or fully based on the soundness of the logic or the validity of the evidence in each argument.