Any device that has a transponder would appear as a secondary target on an airport's radar, since the secondary target is nothing more than a depiction of the source of an RF signal. However, you are connect that it would not likely appear as a primary target. Some of the smaller full-scale aircraft may not even appear as a primary target on most radar systems. Of course, the aircraft must be within line of sight of the radar antenna to be detected, since the transponder's RF signal (roughly 1.0gHz) is generally limited to LOS. Most quads flying at low altitude will not be within LOS of the radar antenna, unless they are somewhere that they shouldn't be.

What is the difference between primary and secondary radar?

Technicalities aside, your larger point is very valid, and far more important. Most airports that have Part 121 airline service have radar. However, the vast majority of airports, including most airports with control towers and commercial operations (e.g. field that cater to private jets), do not have radar at the field. Mandating that all RC/Aircraft to have transponders makes no sense, as that vast majority of these aircraft will never fly close enough to a radar antenna to be detected, even as a secondary target.

I am not familiar with the power requirements of an aircraft transponder. How much power would a transponder require (e.g. how large of a battery is needed) to transmit a signal any significant distance? I have a feeling that most R/C aircraft (and certainly most quads) could not handle the additional weight, unless the technology is miniaturized substantially.