I'm 100 % sure it will work on your console.
With the thrustmaster shifter you had 2 way to plug it in. The USB entrance witch was designed for pc and the entrance that only enters in your steering wheel itself (thrustmaster) for console
But you can also connect the shifter to the console using the usb entrance. Witch means it will be the same. After all it just has to recognize the handbrake and the button it's going to activate. So I'm 100% sure it works on Console aswell.