With JFBConnect, you can setup the
Facebook Requests feature
. That will allow your users to send invitations to their friends and you can define the page the guests will go to as the registration page. Please see the documentation above for the setup, and limitations, of the Requests feature though as Facebook changed how it could be used last year and it's not as effective as it once was.
If you do setup an invitation though, when the user visits your site, you won't be able to get their profile information automatically. They would still need to go through the authentication process by clicking the Facebook Login button on your site. That's the only way for Facebook to know the user wants to share their profile data with your website.
I hope that helps explain,
Alex