I always had a headcanon that the souls inside the animatronics feel whatever the mechanical bodies otherwise wouldn't. This includes pain. But in this case, it's something the animatronic is meant to do (it has a whole mechanism for lifting the face in Parts and Service), so I feel like it would just be a really odd feeling instead.
Now FNaF 2 is a different story, as Bonnie's face was forcibly removed from his possession. So in FNaF 2, Jeremy the MCI kid (not to be mistaken with Jeremy the nightguard or Jeremy the beta tester) would be in pain for a while after the face got salvaged.
