If he’s using his supporting hand in a two hand hold, he’s by definition, altering his grip.
No, he is not, the strong hand is the grip the weak hand merely helps support it the gun doesn't have to move off target if the weak hand is used to cock the piece. With the two hand grip I use I can cock the piece with the thumb of my weak hand without changing the grip itself. I do it all the time with my revolvers, I prefer shooting single action to DA and use the left thumb to pull back that hammer. With practice it is as fast as DA and more accurate.