I would assume not, since Game Freak has been going out of their way in recent games to shiny lock uncatchable Pokémon, such as “strong-looking” Pokémon in the wild area (which are too high-leveled for the player to catch until they get more badges). Even as far back as ORAS, they were already locking the first uncatchable Poochyena you face at the beginning.
I’ve never seen any source that confirms or denies the Pokémon in SwSh’s catching tutorial to be locked, though.