This seems absurdly farfetched for me. It is easy and common for mathematicians to share their work (e.g. on the arXiv) and I consider myself fortunate to get two or three good comments, let alone hundreds. (Of course, this is a claim made by TC, not by academia.edu.) Whatever the virtues of academia.edu or any other technological solution, I do not expect it to multiply the audience for my work by an order of magnitude.
By way of comparison, check out Terry Tao's math blog. His reputation, his expositional ability, and the size and enthusiasm of his audience are surpassed by no one. And of course, the blog (and the ability to comment) are freely available to everyone with a web browser.
http://terrytao.wordpress.com/
Look at the comment counts. For many posts, in the single digits. And this low, even though Tao personally responds to many of the comments and questions.
I suggest that this is likely to be an upper bound for responses to math writing posted anywhere, in any format, with or without restrictions on how can read, write, or respond to what's posted.
I don't think peer review is broken, at least not in math. It can be annoying to do (which is why it takes so long), but we regard it as an obligation and that's why we do it.
The issue, in my mind, is to separate peer review from "publishing", or more to the point, from dissemination. The reason this problem is so thorny and obnoxious (again, in my mind) is that in principle it is trivial.