Well, the xbox does do generic keyboards, right? If you are able to create a proper usb descriptor, i would think why not? Be carefull with your vid&pid, it could still be refused because of these. But, if you can get it to work and want to publish it, take a look here How to get a PID code – pid.codes
Fun experiment though, i have a ‘normal’ s, not a series. But guess that should not matter. Maybe i will try this weekend (if i have a spare arduino that is and if the family allows an experiment on the xbox 
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Cheers!