I think that would cause an increase in volume, but not necessarily a boost in quality. Im sure you know this but amplifier gains are used to match the input voltage of the amplifier to the output voltage of the head unit. If you plugged in a "pre amp" of sorts you would be boosting the voltage. If the gains were set to the previous voltage, say 2.0V, and you boosted it to 4.0V, the gains would have to be adjusted to reflect this change in voltage. You will hear an increase in volume at the previous settings for the 2.0V signal but I would be willing to bet that if you turned the head unit up to near max volume you would notice significant clipping introduced. Due to the fact that the gains are now incorrectly set and the amp is being overdriven, introducing clipping.
I understand what you mean about low quality cables dropping the pre out voltage, and you are definitely correct, I just feel that your use of a "Pre Amp" doesn't illustrate an increase in sound quality. The Pre out voltage doesn't change the quality of the sound, It does however protect from interference. A higher line voltage will allow less interference into the source signal, but will not change the quality of the source.
Also if you feel that I am incorrect please let me know, I don't want to come off as bashing you. I am just trying to make sure correct information is given, as well as preventing speaker damage due to an overdriven signal.