The sensitivity of an audio component to line voltage variations will of course vary greatly among different designs.
I would expect, for example, that a well designed line-level component having a well regulated power supply will generally have little or no such sensitivity. Although even in that case it seems conceivable to me that sonic differences might sometimes occur, for example as a consequence of small changes in internal operating temperatures that would result from changes in line voltage, which would affect the power dissipated by linear regulators and hence their temperatures.
At the other end of the spectrum, though, a tube power amplifier having an unregulated power supply, in which both the filament voltages applied to the tubes and the high voltages applied to the tubes and other circuitry vary essentially in proportion to the line voltage, will have a great deal of sensitivity. In fact Atmasphere has mentioned in some past threads that he has measured a two volt difference in line voltage making as much as a 40% difference in the power capability of a tube amp. And with that difference in power capability a considerable difference in distortion performance seems to me to also be a likely result.
So as is usual in audio, it all depends :-)