I shoot with mine on. I never used to but that was when I had a detachable quiver and it wasn't snugly fit to the bow. I now have a two piece quiver (4 arrow) that is rock solid. I can't think of an honest drawback to having my quiver on my bow. I've been shooting with in on now for a year and wouldn't dream of taking it off.

The quiver is the key to wether or not you can shoot with it on your bow.