Ok, so we got to play with Auto EQ a little at the Cinci meet, and I have another observation about the clicks and pops. It is possible for Auto EQ to try and boost the bass response too high such that the audio stage becomes unstable, resulting in oscillation. In EE terms, it looks it's trying to boost below DC.

This appears to be especially prone to happen in cars with a poor bass response to begin with. Auto EQ still trys to get a response, thus causing the problem. This problem could probably be fixed by capping the amount of boost that the bass EQs are allowed to apply, although I haven't determined what level is safe and what isn't.