No, but odd order harmonic distortion is perceived by the ear as a loudness cue. The amounts of distortion at higher orders may be very small but you will readily hear it. "Turn that down" can often mean turn down the distortion.
Some speaker cables produce lower/higher volume?
I recently auditioned two speaker cables: Audio Art SC5, and Clear Day single silver cable. The Clear Day required a higher volume level on my pre-amp than the Audio Art. Are some speaker cables, LIKE SPEAKERS, rated at higher or lower efficiency which determines volume levels??