I have shot this with my cheek on the foam of the tube. The foam actually helps. The tube never touched my shoulder. My right arm is locked and my left is using the front magpul grips to keep it in place. There is really not much of a recoil to send it flying back to my shoulder.
I'm not sure about shouldering it. I thought I read something that how you shoot it does not change its function. So maybe? Someone else probably has the right answer...