Some transmitters have such a distinct sound that you can identify them with just your unassisted human hearing. Back in my firefighting days, I remember that certain trucks or stations had transmitters where you could identify them from the half second or so of "hum" between the time somebody keyed up the mic and the time they started talking. Using ML / signal processing stuff on a computer, yeah, you can probably get pretty fine grained at discriminating these things.
Now I wonder if you can fingerprint antennas…