I don't have any examples I could provide, but I know there are some sites that have used JFBConnect with squeeze-type pages.
In general, there are extensions for Joomla that allow the creation of squeeze page popups to gather more information. In that popup, you can easily add a Login with Facebook button to the page or any of the other social widgets (Like's, Comment's, etc) with our easy-tags ({JFBCLogin}, {JFBCLike}, {JFBCComments}, etc).
If you have any questions, just let us know,
Alex