It's possible, and something we're investigating for upcoming releases of JFBConnect. The next few versions will be focused on more integration within Facebook and Joomla for things like pushing automatic updates to Facebook and wider integration with different Joomla components. The single-sign on stuff, we've gone down pat, so now it's time for wider integration.
I don't know of any Joomla add-ons that do what you're asking for now.. but if you find any (that work), let us know.