Historically it happen. But does it really pay off? I did it once myself while learning the game but I was just curious at the time. "Golly.....I wonder what would happen if I do this?" type of thing.
The negative is obvious as soon as you change. Lost stability, lost troop moral, lost income, vp loss not to mention your own nation wanting to revolt. Plus all your neighbors are angry at you for cutting off relations. Then there are the neighbors who want to kick your ass. So whats the reason for changing religions?