Yes! This should work exactly as you described! I haven’t personally owned this headset for a couple of months, but I know of no firmware updates that have broken or changed this, and I used to do it myself all the time.
You should have both inputs functioning, and even still be able to chat with your PC as well. In fact, if you’re on Windows 10, you could run a party chat through the Xbox App on PC and still have chat functionality with your friends that way while it’s wired up in this mode. I use this very method as a workaround on the Arctis Pro, currently.
There are only two downsides to this setup. First, your PC (or at least its USB port) has to always be on to power the wireless station if you want to play on your Xbox. Secondly, you’ll hear achievement notification sounds twice: once from your Xbox, and once from your PC. It’s easy enough to turn off PC notifications though, so that one is not really a big deal.
Hope that helps you out! The A20 still has the best pads of any Astro product, and I still can’t believe the A50 continues to be a thing in the face of its much more valuable “little brother.”