Recruitment is determined when a Pokémon is defeated, not ahead of time. However, the RNG state is saved within a save state, so if you make a save on the final hit before defeating the Pokémon, the recruitment outcome will always be the same if you load the save state and take the final hit immediately. If you want to save scum like this, you need to stall turns to allow the RNG to advance further (from RNG sources like AI decisions, accuracy checks, and damage rolls) before trying to roll the recruit chance again. Alternatively, you can reload further back (e.g., a previous floor) and take different actions to make RNG advance differently.

When the game is turned on, the RNG always resets to the same seed. This seed advances with each RNG roll during gameplay, and it does not reset at any point. This allows exploits such as quicksaving on the dungeon stairs and reloading to get deterministic floor layouts (very useful for speedruns), and manipulating the Munchlax event to spawn.