Yes, it would seem so. Xbox UK’s Twitter account confirms “Xbox Series X is backwards compatible with ALL Xbox One controllers across ALL games”. Seems to be a jab to PS5’s compatibility limitations.
The extent of the compatibility to third-party accessories is still a bit unclear from that message, as they don’t specifically mention other peripherals like arcade sticks. But considering the functionality of the controllers is basically the same as the old ones without new additions like PS5’s new controller, it wouldn’t be far-fetched to say they should be compatible.