I have an EFA 4 arrow quiver that I use on my Kanati longbow. It has no affect on the shot. The EFA is so light weight, I hardly notice it, even with arrows in it. I had a Thunderhorn Linx on it and it was too heavy to suit me on that bow. It works real nice on my Dryad Orion though. The Orion has a bit more mass to begin with, so the quiver doesn't seem to be over powering it.
If I'm hunting out of a pop-up blind, I prefer a detachable quiver or a side quiver. It is handier to be able to set the bow down without the nocks sticking in the dirt. From a tree stand or still hunting, I much prefer a bow quiver.
Strap on bow quivers do absorb some vibration, and therefore quiet the bow. I don't think they affect the energy imparted on the arrow, though they do dampen vibration after the arrow leaves the string. I'm not so sure bolt on quivers do much to quiet the bow, at least the ones I've had didn't seem to.
Good question and lots of great answers.