Wouldnt actually work i think. Would just seriously injure the back of your throat.
The kinetic energy of the arrow is zero when he lets go and it will immediately hit a wall which means it never gets to accelerate. So it would just feel like someone is pushing that arrow against your throat with the weight behind it being equal to the draw strength required of the bow. The penetration power of an arrow comes from all the accumulated kinetic energy imparted during the firing being instantaneously released into the target.