This seems like a very fun game, but I'm not sure how much merit it has as a method of determining which side in a debate is the most informed.

Much like the actual Turing Test, it also seems vulnerable to hard-ball inquisitorial tactics. There are probably quite a few questions you could ask which lie outside the ostensible scope of the debate, but which would correlate strongly with a user's true beliefs, or require faculties the respondent simply doesn't have in order to answer satisfactorily. I'm pretty sure if I asked a fake-atheist to name ten atheist-related figures that inspired them, they'd come up with a predictable, odd, or obviously Googled list. Equally, if I was posing as a Christian I'd struggle to name ten inspiring Bible passages that weren't either predictable, odd, or obviously pulled off Google.