Hello forum. New SONOS user here. Also new to HDMI ARC. Sorry if dumb question.

I have: TV (w/HDMI ARC), Xbox, non-SONOS passive speakers.

Can I buy a Sonos AMP, connect it to TV HDMI ARC, connect Xbox to TV HDMI (different input), connect speakers to Sonos Amp, and still get sound out from the Xbox to the passive (non TV) speakers? Not sure how HDMI ARC works. Thanks...