I think the numbers vary depending on the person and the project, but absolutely, having the discipline to push away from the desk and change context puts your productivity in warp gear. It works by allowing you mind to work on the problem while you play.
By the way, to let another secret out of the bag, this process of engineered distraction also works very well with teams.
Many times we confuse stubbornness with determination. Sitting there staring at the screen does not a work product make.
But I'll add one caveat -- the reason I got away from this (and am now only getting back to it) is because the internet itself has become the "getting away" activity. This leaves you at your desk checking emails, updating twitter, etc. In such a case, you're not allowing your subconscious to work on your problem at all. Instead, you're throwing a bunch more stuff at it. So in retrospect I think its critical to physically detach yourself from your technology. A stand-alone game would be fine. Sitting at the terminal listening to your email and IM chimes while you play a flash game would not.
EDIT: It's also interesting to note how hard it is to pull away from your work -- both when you're loving it and when you're hating it. I don't think it's ever easy, but after a while you get into a "rhythm" and it all just kind of flows.