Uh, no it doesn't. I tested it, and it has no effect on the game what so ever. I'm guessing my version must be patched in such a way as to keep it from working. Oh well.
Well that's really weird because my copy of Generals is the one downloaded through Origin. However, it does not work for me. When I press any of the activation F keys, I just hear a Windows ding sound and nothing happens. When I alt-tab out of the game to check, none of the boxes are checked.