Does Power Cord Require Burn-In To Sound Good?

How power influences the sound depends upon the equipment: The power supply in an amplifier could do so thorough a job of filtering out noise along with hum that it might make power conditioning irrelevant. If you use single ended triode amplification it will always draw the same current rather than demand more current for loud passages in a recording and the resistance of a less expensive power cord will be trivial. Higher audio frequencies are easier to filter out than 60 Hz hum and many vacuum tubes have cutoff frequencies at higher radio frequencies.
Watch out for the placebo effect for cables in general. There is some junk science used to market audio.

Be suspicious when the recommended break in period is likely to take longer than the return policy last. Pretty hard to get 200 hours of listening in 30 days for most people. Just a thought. 

Like all audio products, the power cord must burn in for 90 days, i.e. until the credit cardfcannot be refunded.  Ask any sales person who works on commission.

Why is that people with a grudge and an agenda masquerade as audiophiles and get their sadistic kicks haunting and trolling audiophile sites?

To, of course, balance all the unscientific, unproven, useless bull crap that is put out on this forum by questionable sources and to protect the newbie from seeing only the bull crap.  Sorta like walking by a guy beating on a woman and doing nothing about it.

On the other hand.... who praises the significant, if not impressive, improvements in sound quality that can be achieved by buying very expensive "high end” cables? Two groups. Those that manufacture, distribute and sell these products at a serious profit and those who were talked into drinking the Kool Aid and would NEVER fess up to being fleeced. Actually there is a third group. This group gulped the Kool Aid and are victims of the insidious audio expectation bias that causes you to hear the advertised, albeit impossible, sound quality enhancement.

Different power cords do different things to the sound of your system. Without being technical, they have to match your system. Everything needs to burn in, but I agree with millercarbon.