Depends on the ghost and the detector, and who you talk to.
I think it would be a matter of how visible they are in actual light, and not a matter of how corporeal they are. Motion detectors react to changes in light.
So if a ghost isn’t actually affecting light, then no. Otherwise, yes.
Some people have said they’ve seen ghosts and auras etc that others also there don’t see. I wouldn’t think those would show on most cameras.
Some people say they have taken photos of ghosts. If those were the actual camera data at the time, then yes they’d set it off if it was above the threshold for the motion detector to register it.
I’ve seen what looked like figures for a moment where there seems to have been no actual person, in one case in a house with reported ghost. But I don’t know if they were just in my mental or nervous system perception or if there was actually some light to see.