Yup. There's a few sites out there that only allow Facebook logins. Our login module allows you disable just about everything (except the Facebook login button). It's also pretty easy to simply insert the Facebook login button just about anywhere on your site with 3-4 lines of PHP code.
In your Joomla settings, you'd just need to Disable User Registration, and you should be good to go. Just so you know, any users created with JFBConnect are treated just like normal Joomla users, so other components and everything else don't know how the user actually logged into the site.
Of course, if you decide to subscribe and run into any issues with the above, we're always here and ready to help!