It's debatable. I prefer no quiver in a treestand or blind. No torque generated by the off side weight creating cant. I practice all year with no quiver. No need to have the quiver on. You can forget about any time savings by having it on vs having it attached to the tree.

When I spot and stalk I do keep the quiver on. When I commit, I do slide if off the compound before I nock an arrow.

If you're concerned about how quickly you can grab an arrow from the quiver just before you release your first, your mind isn't where it should be. Be sure of your shot, execute the shot and don't worry about the second arrow.