Andy,
I haven't used CiviCRM before, so I don't have a specific answer. However, JFBConnect creates 100% standard Joomla users, so if CiviCRM 'hooks' into the Joomla user database and plugin system as it should, the users created by JFBConnect should be seen just like a user that registers normally. We know some users have used CiviCRM in the past with JFBConnect, but I don't know all the details about their integration.. there have been others doing what you're looking to do, it sounds like.
Hope that answers your question, but if you need anything else, just let us know.
Thanks,
Alex