Yes, these drops are government-funded to some degree. Our YMCA operates a similar thing...they salvage what they think they can sell from donations (pull all of the boards, save good cases, et c.) and the rest gets loaded into a semi trailer for recycling. They take any electronic junk though, not just computers. If I can't give something away, it usually ends up there, unless it has value as metal scrap.
The YMCA here also helps with a local program to provide computers to the poor and mentally handicapped. They're especially big on working CRT monitors, which is great, because those are some of the hardest things to recycle (at least, that's what I've been told by people in the scrap business). I'm sure a few neat old systems get recycled, but in general I think places like these are a good idea.