True, an amplifier uses AC power and there the quality of cord could make a difference. But in something like a CD player where only DC is used, it should not make too much of a difference.
You know the funny thing? The human eye can more easily identify noise and disturbance compared to the ear. Yet, we do not seem to be so worried about connecting the TV using a special power cord. Why simply because it does not make too much difference as the TV makes use of SMPS that handles all these issues. A DVD Player should send badly disturbed images to the screen which is easily discernible.
Take case of a PC. Where each and every but is important, we resolve the issue most times by routing power through an UPS. If power cord could make so much difference, I should be reading HiFi Vision as 'FiHi Sivion' or something. But that hardly happens. Take a printer for example. It should actually be printing junk all the time if power cords could make a difference.
Why do we make so much noise about power cords in an audio system alone? If the designers of these systems realised the issue, I am sure they would taken care to ensure that only clean power reaches their units. Or at least, warn/advise the users as to what is to be done. Would Ayre, for example, when charging 10,000 dollars for a CD player, have found it difficult to add a 500$ power cord if they felt the need? Why would they take the chance of adding a cheapo cord and spoil their reputation? The cord they have used, I am sure, would have been chosen as the best and most justifiable for the player. If they had seen value in a more expensive cord and found it to make a large or sizeable difference to the sound quality, I am sure they would not have hesitated to consider that. If they have cut corners in something as simple as s a power cord, there is something amiss with their design/thought process.
Cheers