After 3 turns, all Pokémon that were on the field when Perish Song was used will faint unless they switch out. Perish Song does not affect Pokémon with the ability Soundproof. If a Pokémon switches out with Baton Pass, Perish Song will still be in effect on the Pokémon switched in, even if it has the ability Soundproof. -Bulbepedia
So no, Soundproof does not affect Perish Song.
Hope This Helped :D