The short answer is yes. You can follow the steps above to get RetroArch up and running on your previous generation Xbox. That being said, you will see a decrease in performance. The Xbox Series S/X has beefier components under the hood compared to the Xbox One/One X. This means that you'll see better performance with the newer console, particularly with emulators that demand more grunt.
Based on our testing, the Xbox One does fine with 8-bit and 16-bit consoles like the Super Nintendo and the Gameboy Advance, while the performance of 32-bit consoles like the PlayStation 1 can be hit or miss. Therefore, if you're aiming to emulate a more powerful console like the Gamecube, you'll see the best performance from an Xbox Series S/X.