Can a power cord increase the resolution of an Class D (SMPS) amp by more than 5% ?

I’m having trouble seeing how a power cord could make a difference.  After all, the stock cable should be capable of delivering the full mains power available to the amp, and the power supply on the amp is going to clean up any minor amount of interference that could possibly sneak in between the wall and the unit.  

Besides, if it was easy to greatly increase the performance of an Amp with a different power cord, why wouldn’t they just ship it with a different power cord?  Why handicap yourself is there’s such an easy solution?   

@atmasphere 

Looking at @dep14 's calculator, it looks like for a typical home-use power cord (16/3 cable at 6' in length) you're only losing .6% of your voltage on a typical 120v 15a home circuit, that seems like it would be well within the margin of error of typical home outlets (which can range from 110v to 130v in actual output).  

Given that amplifiers are typically running at a small fraction of their maximum output (only a few watts except for very short dynamic peaks) how would such a small reduction in voltage actually be audible?  If it were wouldn't you see an even bigger difference between two homes where one's AC voltage averages at 117 volts and another whose voltage averages at 121 volts?