If the games run in a modern Linux desktop with an AMD GPU, they will work on the Steam Deck.
If you add them to Steam, you get access to the granular control over every input. If you don't, the Steam Deck will essentially behave as a Xbox 360 controller.
That's about it, really. The Steam Deck is no different than a desktop PC running Linux.
As for the other distros, they will work, but you'll lose a lot: fan curves will be worse, you'll lose precise haptic feedback, the touchpads will not behave correctly.