The transponder transmits at 1090 MHz, which is well below the band of
most police radars, but you might find a radar detector that is bad enough
that its front end will respond to a 1090 MHz signal. Older radar
detectors had only a crystal detector, so they'd respond to almost any
microwave signal. Or possibly, if the you hold any radar detector close
enough the signal will be strong enough to make the detector buzz if the
transponder is radiating. This assumes you don't have a broadband
RF/microwave power meter. They are available at Radio Shack.

But the transmitter doesn't put out any power unless it is being
interrogated. Doing this on the ground (unless your home airport has an
interrogator on the airport) isn't going to tell you much and in the air (in
a metal airplane) you have a very effective shield between you and the
antenna.

My best bet is that the tube/cavity resonator has detuned with time and is
not responding on-frequency. It is POSSIBLE that the bottle has given up,
but detuning is the bane of vacuum tube transponders.

Jim