I began shooting with the quiver on when I started shooting a Mathews and have not changed. I think the added weight of the two piece on the ends of the riser adds a little forgiveness. Noise has not been an issue. As far as accuracy I don’t notice any difference between a full quiver and an empty one inside 30 yard and at 40 it is negligible. Also, keeping it on means one less thing to get ready once I climb the tree. I have needed a quick reload for a second deer!
Due to the fact that I travel to the stand with the quiver attached and I may well see a deer on that trek , I choose to set up the bow for that possibility.
Since the bow is set up that way I leave it on.
I have the 2 piece and hunt with it on. I’ve been shooting all spring and summer with it off but just two weeks ago I started shooting with it on just to get use to the weight difference. To be honest with you I like shooting with it on better.
I keep mine on all the time because I don’t like to change the feel of my bow if I’m practicing, in a tree, on the ground ect. Also it’s handy having arrows on the ready, especially on the stalk. I use the fixed model Arrow Web and it’s silent. It also holds my arrows firm so they don’t vibrate or make noise. I have noticed other quivers that really hum with vibration so I could understand why some do and some don’t.