However, I expect the entire world to know any time I accidentally follow a link to academia.edu. And I especially expect that academia.edu will try their damnedest to figure out who I am and sell that information to someone. Put simply, academia.edu feels like linkedin.com.
This juxtaposition is going to be a huge issue for academia.edu if they try to get into the peer review software game.
I would sooner not participate on an editorial board/program committee than use academia.edu to submit a blind review. I simply would not trust a platform associated with that site or its parent company to take privacy seriously.
I suspect this attitude is fairly common. Linkedin/Facebook/Academia.edu exist solely because privacy isn't perceived as more valuable than the services provided. But every academic I know is extremely serious about protecting the anonymity of reviewers.
If you want such a product to succeed, you'll need an extremely strong pro-privacy pitch (backed up by The Truth) along the lines of "your data is used for exactly nothing other than displaying peer review results for this particular paper to the authors and the other board/committee members".
Especially since most academic's perception of academia.edu is "that site that lets me see who reads my papers."