Does a higher gauge electrical wire impact voltage level?

Most amplifiers are "unregulated." Meaning long term (several seconds) changes in the AC line will make it to the amplifier voltage rails. So if your DC rails are +- 50V with 120VAC input, they will vary in proportion to input. They could be 45V at 108V for instance (picking values that are 10% for ease of math).

And,

When the power transformer’s secondary winding voltage is lower feeding the rectifier, due to a quick AC mains VD event, and the electrolytic capacitors voltage is higher, the rectifier will not conduct and the caps do not get recharged for that "(millisecond pulse)" in time. Or for a longer VD drop, until the caps voltage is lower than that of the AC voltage feeding the rectifier.

Also when the mains voltage drops below the manufacturers rated AC voltage the power output of the Amp's wattage will be lowered.

Silly question.  Just make sure you have a thick enough wire and voltage changes will be tiny.  And, unlike many here who worry too much about it, remember your power cord is the last 6 feet of miles and miles of electricity company cable bringing your power from the power station, plus a few 10s of feet in your home wiring.

Don't obsess.

clearthionker +1.

When the power transformer’s secondary winding voltage is lower feeding the rectifier, due to a quick AC mains VD event, and the electrolytic capacitors voltage is higher, the rectifier will not conduct and the caps do not get recharged for that "(millisecond pulse)" in time.

@jea48  Yes, but this happens all the time. The capacitor's job is to integrate the incoming peak voltages over time. When idling and fully charged, the window of time when the rectifier is conducting is already pretty narrow.  It only conducts on the peaks of the 60Hz waveform.  The capacitors charge, and then, until the next cycle, continue to discharge.  Hence the natural ripple seen there.  If the mains VAC is now a little lower, it may not charge at all, or for a shorter period of time.

So the output of the power supply is in constant flux, especially if you consider how it discharges during musical playback of signals much faster than 60 Hz.  Kind of amazing it works at all. :)