No. It only checks the Pokémon you're going into the GBU with.
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I have a question, but I can't find a way to straight-forwardly ask it, so I'll propose a scenario:
In a DOUBLE battle, First turn, I have a Weavile and a Ludicolo vs XXXX and XXXX. I Fake Out both opponents.
Turn 2, I switch out Weavile to get a Drizzle Politoed in. Ludicolo uses Surf.
The question is, Will Swift Swim get activated and Water moves get the boost on the same turn or until the next turn???