No, actually replays are only the recording of in-game events; the replays does recalculate them again (which is why they can be infamously incorrect). The AI doesn't need to do any decisions anymore, so that should have an impact on the performace, but my guess is that's negligable, at least as long as you only have one opponent.
I'd say the FPS is mostly influenced by how many units are displayed, at what level of detail (zooming in violently breaks the framerate), particle effects, and maybe how much the camera is moved around; so replay FPS should be comparable to in-game.