If you believe a power cable makes a difference, and you believe you hear a difference, then be happy. I will not tell you what you can or can't hear. I am neither that arrogant nor disrespectable :)
Now as both a subjective audiophile and an engineer:
Yes, they can bleed 60 Hz and harmonics into poorly shielded signal cables.
Yes, many cheap cords are not even twisted inside to minimize emissions.
Yes they can pick up RF
Yes, I have found cheep cables that were not even welded to the prongs, Just held in place by the overmould! YIKES!
As with any cable, the shorter the better. The appropriate gauge, the better. Twisted the better. Separation from signals the better.
BUT, OK, several hundred feet of ALUMINUM entrance wire, bi-metallic contacts in the breaker, hundred feet of the cheapest copper you can find in your wall, that "magic cord" and then going into an alloy fuse, tin plated fuse holder and into several hundred more feet of cheap copper in the transformer or whatever they do to it in a switching supply, the ultimate RF generator. So, is that where you want to spend your money? I spent mine on some replacement ends so I could shorten and tidy up the cables. I also have a Emotiva DC blocker as I DO get transformer hum depending on how many LED lights, dimmers and DC fans are running. Transformers are the very best RF filter there is. I love linear supplies.
Some even suggest "audiophile" outlets. Well, there are three actually different outlets. The 49 cent "contractor" ones with back-stab. Total garbage, swap them all out. Then the mid grade $1.95 with much stiffer holding power and a little heavier, followed by the $4 "commercial" grade. What my house if full of. Snug fit. Good contacts. Don't fatigue. These can also get "medical" separated ground or "data center" which as far as I can tell, differ in the orange or green dot only.
Your choice. The only risk is some esoteric "audio" cables are not UL/CSA certified so you are on your own to know if they are safe as far as not starting a fire.