I believe so. I think there are many factors though. Deer pressure, bow noise and even foliage. It seems one can hear much more in the woods in late season after the leaves have fallen as a posed to late season. If the deer is already on edge then it's going to react much differently to what ever noise level of the bow.
If you are asking does the speed get it there before it has time to jump, then my answer is no, the arrow is not fast enough to out run the deer reaction.
A hunter is not a man who kills animals but, a man who holds immense knowledge, loves, respects and takes great steps in the preservation of the creatures he harvests. He is loyal, grateful, responsible and ethical in every aspect of his chase. He is who I strive every day to be.