I'm not sure you need to turn to extreme/defective cases to find examples of amps that have what would generally be considered to have quite acceptable levels of THD, but with enough of it higher order to question whether it really would be inaudible.
Here's a quick side-by-side of Stereophile's measurements of two amps that have similar THD. The amp on the left has its strongest harmonic (the 3rd) at around -76dB, a bit of 5th and a touch of 2nd and 7th, but nothing much above the noise floor beyond that. The amp on the right has its strongest harmonic (the 2nd) at about -79dB (so, lower in level than the strongest harmonic of the other amp), but then has a string of higher order harmonics out to (apparently) infinity, all between around -90dB and -105dB.
I'm just eyeballing these graphs obviously, but both amps look to have about the same THD (the determination of which will always be dominated by the strongest one or two harmonics). Still, I'd say the amp on the right is more likely to produce audible distortion than the amp on the left, due to the higher order harmonics being so many and being 25-ish dB higher in level.
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