Phil,
Alright, we've done a bit more testing and setup a (very quick) test site to play with Authenticated Referrals. You can view it at:
apps.facebook.com/jfbconnect-rocks/
That's using a completely unmodified version of JFBConnect v4.2.1, and it seems (to us) to do what you're looking for with automatically logging the user in. It doesn't have a separate flow for users registering through the site itself, but that really shouldn't affect the authenticated referrals bit.
For us, on that site, when we first get the authentication popup just for visiting, an account is created for us and we are immediate logged in. Later on, if we return to the site, we are automatically logged in. Right now, the only oddity we're seeing is that if you log out and then immediately try to go to the page, it doesn't necessarily log you in. The cookie from Facebook isn't being destroyed properly.. we're looking into it. However, if you clear your browser cookies, log into Facebook and then visit the page, you should be auto-logged in.
Let us know what you see, and if it is/isn't what you're expecting.
Alex