This is a difficult question to answer because harmonic distortion can resemble the harmonic overtones created by musical instruments (including the human voice).
The distortion produced by electronics may be hidden by similar harmonic content that is naturally produced by the musical instruments. However, if the distortion level is too high, the musical instruments will begin to sound different than they do live. The distortion threshold where an instrument begins to sound different will vary significantly depending on the instrument and on the complexity of the musical performance. The best that we can say is that the system distortion may be masked by music.
If the masking is partial, the distortion can change the sound of the instruments, change the apparent EQ of the recording, blur the stereo image, and add clutter and confusion to the overall presentation.
Certain instruments are very difficult to reproduce because the overtones produced by the instrument are not exactly the same frequency as the harmonic distortion produced by electronics. These electronically produced harmonics are poorly masked when they beat against the overtones produced by the instrument.
The piano is particularly difficult to reproduce since the overtones are stretched slightly above integer ratios to the fundamental tone. These stretched overtones beat against the exact integer ratios produced by electronic systems.
Music is also much less effective at masking non-harmonic distortion such as IMD, jitter sidebands, and digital aliasing. These non-harmonic non-musical distortion components have no correlation to the overtones that are naturally produced by musical instruments. Consequently, these forms of distortion are much easier to hear when playing music.
Music has absolutely no ability to mask idle channel noise, because this is noise that is present when the music is not playing.
System noise may not be noticeable while the music is playing, but it may still obscure some of the low-level details in the recording. In other words, the system noise can partially mask the music if the noise is too high.
There is a threshold at which noise and distortion are absolutely inaudible. This occurs when the noise plus distortion is reproduced at a level that is below the threshold of hearing at the listening position. The threshold of normal hearing is about 0 dB SPL. Therefore, if we can reduce the system noise and distortion to these levels, we are no longer dependent on masking. In other words it would be impossible to hear the distortion plus noise, even if we could play these while the music is off.
Reducing the electronically generated THD+N to levels below 0 dB SPL is entirely possible with today's technology. In fact, all Benchmark electronic audio products are designed to keep the electronically produced THD+N at or below 0 dB SPL. The combined THD+N contribution of the DAC, preamplifier, and power amplifier will be less than 0 dB SPL at the listening position. This calculator can be used to confirm this fact. It can also be used to determine how low THD+N needs to be in order to achieve absolute inaudibility.
The only remaining distortion will be the distortion produced by the loudspeakers (definitely audible) and the distortion plus noise in the recording (often audible). When the playback electronics are clean, variations in recording quality are quite noticeable. Likewise, the differences between speakers are also more noticeable.