Based mostly on Unnamed's comment regarding a poll on homosexuality, I expect it would be lower than what you found for self-selected interested respondents, but I don't have much confidence in this, and I'm not familiar enough with AQ variance to say how much lower.

I have some experience with trying to do survey research right (i.e. in a manner that results in true conclusions about the population), and I have seen so many ways that convenience samples can make me wrong (non-response bias is just a start), that I generally don't bother much with trying to correct for one particular bias. Instead, I stick to random samples or use estimators that can handle convenience samples. But I am genuinely intrigued by your idea (from the very end of your post) to use a prior on non-response bias and a prior on AQ distribution to estimate the true AQ distribution of LW users. This wouldn't handle e.g. problems with question wording or lies in responses, but I would expect those problems to be small in comparison to the non-response bias. Could you elaborate, or point me to any survey methods papers that explain this approach in detail? Where would you get the priors?