>I suppose they could have roving bands of listening posts looking for the uplink signals.

I think this is pretty likely.

In the US the FCC has a whole set of systems designed to locate interference sources [1], and I've heard stories that they're extremely good at it. They even have a whole facility in Maryland dedicated to satellite monitoring!

[1] https://www.fcc.gov/over-air-spectrum-observation-capabiliti...