Maybe
I'm willing to take your word for it, and obviously the more thrust you can put out, the easier the results will be to detect and analyze. But I have seen NASA and others use radio signal analysis to detect astoundingly small changes in velocity and/or position. Gravity Probe B had a positioning system that was almost supernatural.
For all I know, even a very tiny thrust might create enough change in trajectory in a multi-million-ton rock to be detected by sophisticated systems. Bring lasers into it somehow, and chances would be even better.