That should work just fine! Are you connected through an optical cable then? Just make sure to select the “HDMI or Optical Headset” option underneath the Dolby Atmos setting in the Xbox options.
Also, make sure to turn off any surround processing on your Astro Mixamp, as then you’ll be interfering with the Atmos signal. That processing is designed to accept a Dolby Digital output from your console, whereas with Atmos all the processing is done on the console itself then just pumped to your headphones. So you don’t want the mixamp to get in the way.
Hope that helps you out!