Even harmonic distortion is considered in some circles to "sound good". I have met one person who liked lots of it - he had cobbled together a "wonderfully hifi stereo" that was full of it.
It does not get past the first series capacitor or transformer though, although in the case of a transformer, that counts as a "stage" for the purposes of introducing distortion.
Not sure what the residual effects on an audio transformer are. It is not something I would want to do without being sure it was not going to permanently magnetise the core.