They get boosts in the rain, so it would make sense if they did underwater as well.
No Underwater does not give any boost to water Pokemon. It would be sorta unfair if it did as Theres no way to change It from underwater unlike rain.
Actually, some Pokemon do get boosts when surfing. Only two Pokemon get this glory. Kyogre and Sharpedo. Kyogre moves faster than normal Pokemon (I believe 1.5 times faster) when surfing, and has a larger hitbox when going underwater. Basically, he is larger. Sharpedo moves twice as fast than normal Pokemon, but you can't fish when riding him. Hope I helped!
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