Actually, I can see that working, because as the carp sucks in the bait, the hook will follow, just behind, at the right angle to hook the fish. I think this would work best with a critically balanced bait, 'coz I think a pop up would mean the hook would float in the top of the mouth, a bottom bait would drag along the bottom, which may catch hold, but the critically balanced means the bait would be above the hook, with the hook hanging down.
Heres a tip, get a piece of straight pipe about the diameter of a carps mouth, then cut the end so its about a 45 degree angle, and stick some small strips of foam on the angled end of the tube, on the inside where the fishes lips would be. Lay your rig out in a fishtank, then put one hand over the straight end of the pipe, so it's airtight, then position the 'mouth' over your rig, and move your hand, as the water rushes in to replace the air the rig will be sucked in, and you can see how effective the rig is in a real(ish) situation. If you didn't understand that, you never will, it's hard to explain