I think the idea is really cool and I can see how useful it could be for companies, but do you have evidence that users actually give feedback via your method?
I'm trying to look at this product from that side of the equation, and I could see me getting frustrated that clicking "Sign up with Google+" doesn't actually do that. If you have evidence showing that users are willing to give feedback, or have some type of insight regarding that, I'd definitely include it in the application.
Goodluck!