My experience probably doesn't 'count' because I average 5 - 7 movies a month, so I likely have never been "throttled," but it's never taken more than two days for me to get new movies (I send one back Monday, get the next one always by Wednesday). And I've always gotten the next selection on my list, whether it's popular or not.
I've had some busy months where I might have gotten ten movies, and never saw a difference. But even that's probably not much.