here is the deal, and its a basic principle law of sound travel.
at 300 FPS your arrow is going roughly 204 MPH, while this isnt breaking the sound barrier, it is fast enough to keep the arrow neck and neck with the sound at the ranges you are shooting. So hearing the arrow go by is very normal, wheras if you were to stand directly in the flight path (which i would not so much recommend) you would not hear the arrow.
another interesting phenomina is the wind moving past the arrow helps push sound further behind it.
but with string noise, it is a sound wave, that leaves the bow at the same time as the arrow, that doesnt have any other factor working against it. so it gets to the deer slightly before the arrow does, which is why we workto make our bows more quiet, more so than making our arrows quiter.

so in short, no arrow noise does not spook deer, it is a concept that has been visited and disproven in the past. but it was a good thing to discuss....now if only we could have asked the question more maturely