Yes it will.
They are exactly the same thing. The controller for Windows just comes with a USB receiver that you can plug into your computer. Once that receiver is plugged into the computer any 360 controller can be paired with it.
EDIT: What I mean is that the Xbox 360 controller that comes with the "Xbox 360 wireless controller for Windows" is just a regular Xbox 360 wireless controller, it is the separate USB receiver that makes it work with a PC, and if you look around you can find 3rd party USB dongles that will make any Xbox 360 controller work with the PC.