I have an alpine archery 5 arrow quiver and I ussually keep it on while hunting and shooting. It's low profile so it does stay out of the way. Apine archery also utilizes a rubber mounting bracket that in my opinion works to dampen vibration. I shoot an 70# Mathews Sq2 and constantly get complimented on how quiet it is. Who knows that may be the reason?
It's a matter of personal preference, my preference is to shoot with it on.