Theoretically, YES, AGC and DRC introduces non-linearity into your audio.
Say you implement AGC or DRC in your nice audio system in a nice sound room. You sit down in the nice couch, have a glass of fine wine and start playing your favorite classical music piece, eg. Zigeunerweissen by Sarasate.
Suddenly, you will realize that Zigeunerweissen sounds weird, in fact it is almost monotonous and boring (certainly not worthy of a Masterpiece by Sarasate!!!) & no amount of fine wine can make you feel better!
Well, it is simply because DRC has compressed the dynamic range significantly and in the extreme case, everything sounds the same volume (certainly not how Zigeunerweissen should be played!!!).
HOWEVER, that is not how AGC or DRC are supposed to be implemented. AGC and DRC are typically used in watching movies or playing speech audio, or music playback in a non-ideal environment (eg. in a noisy car, train etc). The idea is to allow you to hear all the details of softer signals like footsteps, the rustling of the leaves, and yet not blow out your ears with the loud signals (like explosions). More importantly, AGC And DRC avoids the nasty distortions from clipping.
For more details, read the previous post from me on AGC and DRC.