Yes, it should. JFBConnect is still compatible with both Joomla 3.x and 2.x, though we don't test the 2.x features nearly as much anymore. I'd recommend upgrading JFBConnect on your Joomla 2.x site, then upgrading Joomla, then re-installing the latest JFBConnect once again on your 3.x site.
I hope that helps get you going, but should you need anything else, just let us know.
Thanks,
Alex