Can is a bit abstract. I've found it works really poorly in the browser ( just getting to the correct page that actually shows you the list of games available is a pain and requires multiple hops).
For what it's worth, I used xcloud for the first time on iOS this morning, where it runs entirely in the browser. It actually wasn't bad! I had to close out the browser entirely and reopen it to fix issues with the streaming, but once I did that it was much smoother than I anticipated, and jumping into a game was quick.
It was absolutely unplayable without a controller, mind you, but it worked.
You can run Game Pass directly in a browser. So you could use GamePass on really any modern web connected device.
I would be shocked if Microsoft supported the actual GamePass app on Linux