JFBConnect could definitely do it. It depends on what you want to do... let the account be created but not activate it if not in the right group, or just deny the registration altogether. If you are ok with denying the registration, you can modify the autoCreateUser function in the models/loginregister.php file. The check for the user's groups is pretty simple and we already do it in the /components/com_jfbconnect/libraries/provider/facebook/channel/fields/facebookgrouplist.php file in the getOptions section. From there, you can parse through the user's groups and determine if the right one is set.
That's a very high-level overview but hopefully it helps get you started,
Alex