i personally dont believe in them hearing the string persay. i believe it is the arrow and BH itself.

But for the most part for your original question. for this instance. the speed of sound would still travel at a constant speed. therefore you would think that the sound would reach the deer at the same time. so why would they not jump it this time.

In a dry air situation at approx. 70 degrees the speed of sound is around 340 fps. so the sound of your string is almost gauranteed to beat the arrow. at least under 20 yards. the thing is that at 30 yards you get more "objects" in the way to slow it down. so the arrow has a possibility of reaching the deer before the sound of the string.