I'm aware of a controlled listening test in which 30% second harmonic distortion was statistically undetectable
Second harmonic is fairly benign but 3rd harmonic is bad - so it depends on the type of distortion. The other issue is that 1% distortion at the 3rd harmonic of a 20 Hz fundamental will sound nearly equally as loud as the fundamental note itself due to your increased hearing sensitivity at 60 Hz compared to 20Hz (see Equal loudness contours). So in the end, a distorting subwoofer simply populates the bandwidth where your hearing is much more highly sensitive from 60 to 180 Hz with audible response. This is may be quite the opposite of your original intention when buying the sub - which was to augment the bottom octave rather than overwhelm the 60 to 180 Hz range.