It's not my thesis that the 2nd and 3rd order harmonics are audible - but rather that the power they consume by the amp affects all other frequencies across the spectrum - and this is what gives the tubes their tubbie-ness. Just a thought.....
They can't .. and the 'power' consumed by harmonics is 40dB or 60dB lower than the original signal (you would need an amp with shitloads of distortion for that)
To get an idea... assuming a headphone amp with 5mW average power draw (decently loud) the 'power' of the harmonics will be in the order of 10
μW or so (max)
Also the harmonics won't be audible with tube amps because mostly they will be 2nd and 3rd mostly. All instruments/voices etc have harmonics that will be higher than what an amp will add.
The harmonics are not the problem with amps. That will not make anything sound better or worse. The biggest issue is inter-modulation distortion.
With harmonic distortion there will always also be inter-modulation (as soon as more than one sine wave is present which there always is).
These create frequencies that are not harmonically related and can fall outside of masking by music (with certain recordings) and these are never ' pleasant' nor 'increase sound quality'.