Yes, one of the problems with new magicians is that they try to show everyting clean even when they don't have to. I have two friends that aren't really into practicing tons of magic, but they enjoy the occasional trick. Just today as they were practicing an effect for me they said "Ok, so look, just an ordinary quarter. Nothing changed." I stopped them right there and told them not to do that. Its not necessary in that situation. It only opens up the possibility of trickery going on in the spectator's mind. If that possibility isn't brought up, suspicion is not there and it will make your performance a lot better.
Again, I'm not sure if the cap can be signed, but I honestly don't even care. I wouldn't have them sign it even if it could be signed. In this case, it only brings up the possibility of suspicion.
-Doug