On a bow shooting 150 fps, an arrow reaches it's target at 20 yards in approximately 0.4 seconds. It takes 0.05 seconds for any sound from your bow to reach the deer (speed of sound being approx 1126 fps). That gives the deer 0.35 seconds to react to any sound your bow or arrow makes. Research indicates that reaction to sound stimulus is about 0.1 to 0.2 seconds in most animals - faster than visual stimulus.
So any deer can react in time to at least begin bunching it's muscles for the jump to almost any arrow - even one going very fast. The question becomes, is that sound enough to trigger its reflexes? Will the sound prompt a reaction? The only way to tell is by shooting the heads and observing the deer's responses.