Generation 9 Obedience question

I am aware that in Scarlet/Violet, Obedience works differently than in past games. If you catch a Pokémon that is over level 20, it will not obey you if you don't have any of the Paldea League Badges. What if you catch a level 5 Pokémon and level it up to past 20? Would it still obey you?