In York (UK) it is a mixed bag. There are a couple of simple pedestrian crossings near my home where the lights never change without a press and change very quickly once requested. At junctions it is more complex and seems to vary: some definitely have their sequence altered by specific pedestrian requests, some definitely seem not to. I've not noted if any vary by time of day, as some people report.
Any crossing near a school will generally change very quickly after a button press, but only during the school-run hours. Knowing which these are can noticeably accelerate ones journey to and from work.
There's a light near my apartment that takes about 4 full minutes to change (it's a small-road-onto-big-road intersection), at all hours of the day. However, the walk light changes the light instantly.
I leave for work around 6 each morning, when there's nearly no one else on the roads. Since it's so frustrating to watch an empty road for four minutes, I have actually gotten out of my car, hit the button, and gotten back into my car to accelerate the light change.
