No it doesn't.

Microsoft locks down all wireless connections to the Xbox platform, requiring a paid license for their proprietary Wi-Fi Direct-derived system. This is why there are so few wireless Xbox headsets on the market. It's not worth it for companies to pay a premium to support a smaller user base.

I wrote more about this here: https://xander51.medium.com/microsofts-big-xbox-audio-mistake-71505042af2d