It works...

xbox360 controller for windows / for xbox360 console is the same...

if you want to use on windows, you need the wireless receiver, and driver (all you can get from xbox360 controller for windows )

and the the one that you bought for windows also can be used on your xbox360 console.. vice versa..

if you have the play & charge kit, try connect it on your pc.. your pc will detect a new hardware, xbox360 wireless controller via play & charge kit (or something like that..).. windows can obtain driver automatically from internet..
but using this method, i'm not sure if you still need the wireless receiver.. at the time that I try, I didn't disconnect the wireless receiver..