Yes, Rust Console Edition does have a public test branch. This is currently only available to those who pre-order or purchase the Deluxe/ Ultimate versions of the game.
The public test branch will be available to Deluxe and Ultimate edition buyers in the coming weeks when we have the first major patch ready to test. You will be able to access this through your Platform Dashboard, similar to how you start the base game, it will be called Rust Console Edition - Public Test Branch.