Possible or not possible?
There's currently no option within Friend Connect to do this. I don't
know that we have any plans to ever implement access control, but if
you don't mind the fact that a clever person could easily circumvent
it, you could just simply not display any friend connect gadgets to
people who don't have the Friend Connect cookie. Then only give out
the sign-up page to people you invite. Since you can ban members,
this should work well enough — just ban anyone who circumvents the
system, if anyone even bothers. I highly doubt anyone will try.
-Bob