[@rocketrobie2][@Keyblade87]From studying Goku, I think he would have found out about him transforming at the Tournament and Roshi blowing up the moon to stop it.  He might also have seen Gohan transform while Picollo was training him, so I'd say yes. They do know about it but never had to worry about it as most of them don't have tails and the environment has no real moon.