A quick search shows it's been tried already, sort of, but hasn't exactly taken off:
https://bitcointalksearch.org/topic/bitcoin-appcom-facebook-bitcoin-app-001-btc-welcome-present-69071
http://pierreterre.com/blog/how-bitcoin-may-undo-applefacebook-30-sales-tax
https://en.bitcoin.it/wiki/Bitcoin-App.com
It seems like the idea so far has centered around the concept of sending bitcoins unannounced to people who don't know much about them and then hoping they'll use them.
I think it might do well by simply being an Instawallet-like service that makes it easier for people who already use bitcoins to send them to others on FB who also already use bitcoins. You would have to be signed up already to receive the coins, and then the system just transfers the funds internally when sending to someone else within the system. Charge a monthly rate (in bitcoin, of course) to use, possibly pre-paid, and it just might be profitable too.