XBox 360 controllers are compatible with PCs (with the appropriate drivers), and Gamestudio has gamepad support. So you can build a PC game that uses XBox controllers, but the engine has no direct support for Xbox 360.

I've been told that Conitec's official answer to this question is that they will port any 3D Gamestudio application to the Xbox 360 if it has already been released for the PC (if the developer wants it, of course). But I'm not sure about that policy.