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If the inhabitants of a universe with atomic NP oracles developed a computational complexity theory which accordingly considered performing an NP oracle operation to be O(1), then their "P" and "NP" would be analogous to what we call "P" and "NP", but they wouldn't be the same objects.
Sure, hence merely "play the same role". Note that analogy for P in NP-universe is NP-hard, not NP.