Category ungating and brand ungating are two separate things. So no, getting ungated in the category does not ungate you for the brands in that category. For example, if you wanted to sell a Nerf product in the toys and games category, you would need to get ungated in the category of toys and games, and then also get ungated in the brand if the brand requires ungating.
Do categories ungate brands?
Can a brand get me ungated in a category?
Will approval in a category allow me to sell brands within that category?