The electronics for your typical GA transponder are primitive by modern standards and can be very small, but it would probably need to be paired with a radar reflector or else it would either remain undetected or appear as noise.
Older style (I forget the proper name) transponders don't indicate their position, only ID and altitude. Newer ADS-B transponders include GPS position.
It's an interesting point though. Assuming for a moment that a bunch of drone operators equipped their drones with ADS-B transponders, I speculate that there could be a chance of overwhelming an airport approach radar's ability to track targets. Could potentially overwhelm the electronics, or the operators.
Do that and keep doing it, and it would not be hard to find your transmitter.