It's a lot harder to detect spacecraft manoeuvres than that. Depending on the type of thruster you might have a chance of detecting it if you have extremely sensitive, very expensive equipment closely monitoring a specific satellite in LEO, but nobody has enough of those to monitor every satellite, or even every military satellite constantly. At the distance of the Moon, forget it. No Earth based telescope can even resolve Chang'e 5 at all at this range, let alone a thrust plume. But even in LEO observing from another orbital sensor it's not easy, if the thruster is on the far side of the satellite, or using cold gas thrusters, or your view of the thruster is sufficiently blocked by a solar panel or antenna, also forget it.