I'd say it might break the camera due to the recoil. Also, the actual shot will not be captured on the video because as it recoils it will drastically move the camera lense. It's a good idea, but itll be tough to keep the deer in the screen after the shot.
I've seen a bow mounted camera jump so much after a shot that the deer moved out of the screen.
Kool idea though, good luck with it