'Harmonic' is meaningless on a complex signal unless you can break it into monophonic tones and apply harmonic distortion to each tone individually, so the term is meaningless when a harmonic distortion effects box is applied to a complex, changing, composite signal. What is really meant is 'bent transfer function'.
Sure it can be fantasised about as a musical frequency domain process, but in reality it is simply what you get when you warp a complex signal with a dumb curve in the time domain. Clearly, the difference between linear and 'bent' is wholly dependent on the interaction between the signal elements so it really is all intermodulation distortion on everything but very specific signals.
In the studio, where the producers have access to the individual elements, then application of distortion to a monophonic source may be an interesting creative effect. The consumer with his valve amplifier only has access to the composite recording, however.
Perhaps this effect may be one of the main reasons for systems that are supposedly 'good' at pop but 'bad' at classical, etc. Varying degrees of offensiveness dependent on signal complexity and content.
As you can tell, I'm sceptical about 'euphony'!