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I did some checking and testing:
>Using a cheat to see the enemy's HP reveals that yes, they are using the stats corresponding to the original level. Natures can be different, though.
>In practice the difference isn't that egregious because the actual level value (the number) does play a part in the damage calculation. In case of Iris' Druddigon, the stats remaining the same as level 57 is roughly equivalent to battling against a level 63 Druddigon with worse IVs.
>When using cheats and catching the trainer's Pokémon, they revert back to the Normal mode levels.