Does Xbox support wireless headsets?

There’s this headset I’ve been eyeing, you just plug the usb into your console and it should work wirelessly (for PS and PC). Somebody commented something along the lines of “too bad it doesn’t work on Xbox” which got a reply by somebody saying “it works for my cousin”. I was wondering if someone here could confirm since I don’t want to go based off of word by mouth. I should also say that the box does say it doesn’t work with Xbox, but I’m not very techie so idk if Xbox is able to just update their console to fix it or anything lol.