G-Sync monitors of this generation are hard-limited to 60 Hz over HDMI. He will need an adapter to connect to the DisplayPort input to get 120 Hz. Support will depend on whether the monitor's 120 Hz profile uses standard CTA-861 timing, which we can have OP check for.
If that's the case chances are even slimmer. OP didn't mention using GSync or Freesync. OP will at very least need an active adapter and hope that adapter works, even then it's not guaranteed to work.
Out of 4 monitors I bought only one worked with the Xbox despite all having HDMI 2.1 ports, so that's modern monitors with properly spec'd ports (bad EDID tables were why they didn't work) not working because Xbox's are SUPER picky. All other devices worked fine but the Xbox gave me the finger.
A spaghetti nest of cables and adapters for what the OP wants to do is a 50/50 shot and only worth it if they are willing to invest time and have the ability to easily and hassle free return parts if they don't work.