If you decided to PM everyone right after you got your role, I guess you could be extremely lucky and get a new player to reveal he's a G. That's going to happen 0.01% of the times though. More likely everyone will suspect you because of your strange behavior. :D
The G's already know who the other G's are (the narrator tells them), so I can't see how a C would trick his way into the G conference. :D Plus, how would the C know which players to contact? :D