Littlefield,
I know it seems like all radar detectors do is just listen for the right frequency of radio waves from the radar guns. But they do emit their own electronic signatures.
In England, BBC is commercial-free because there's a charge for each TV set. So there are trucks that roam around sniffing out the electronic signature of TV's.
The computer monitor you're now looking at is sending out an electronic signature that the right equipment can listen to and know exactly what's on your screen. Check
www.bbc.co.uk/dna/h2g2/A4075463 for an interesting description of electronic spy measures and countermeasures.
States and countries that ban radar detectors can indeed detect them just by listening.