Unfortunately, I don't think what you're looking for is doable. There are many calls available within JFBConnect, but they all go through Joomla and there's not an API with GET/POST calls you could use to log a user in or perform other functions.
If there's something else you're looking for, please let us know the details and we can let you know if it's feasible.
Finally, I apologize for the lengthy delay. We had an issue that was preventing us from responding to support requests but it is rectified now.
Thanks,
Alex