That is what they advertise at Nutty Buddy. I have had it preached to me tho that if you must wear a jockstrap and compression shorts, then the jock goes on first. Otherwise when your legs move and the crotch of the shorts moves down (thus the inherent problem with compression shorts) it will pull the jock or cup jock down also.
I have one old cup that had foam padding. instead of the more rubbery like most cups today, and it works great for going jock, cup and comp shorts. The newer ones pull the hair and your skin. These newer cups is why I had to cover the cup some way, i.e. by cutting the pouch off a cup jock, thus the cup is covered and you can wear jock first, then compression shorts, then just put the cup between when you need it.
If I ever see a guys wearing compression shorts over boxers I will call him out for the moron he is.