Certainly this hasn't been proven with apps off of facebook. It's an excellent experiment though.
If you really want to grow even faster:
1) scrap the standalone website and build it as an iframe app (should be very little work). This will simplify login significantly and will keep people inside FB, which in my experience, makes a world of difference in the viral funnel.
2) replace the "share this link" with a real Stream.publish call. Consider adding like buttons for every single user's page.
3) Allow people to see which of their friends have answers as well.
Then, if you add the 1 credit transaction, you should do pretty well. Beware, however... Facebook has given out a lot of free credits to users and they do not give app devs any payback when free credits are used. These chargebacks can affect actual revenue from small transactions like this significantly.