There is something that may cause a powercord to affect the sound, and that is the amount of filtering the equipment has before it reaches the power transformer. A lot of equipment has none, but others have at least some amount. The Saskia turntable controller is bandwidth limited, so that the CPU remains free from any line influences, whether real, or imagined. The mains is heavily filtered before it reaches the power transformer. Earlier models were not bandwidth limited, so we did, of course, notice differences in incoming power. That's what started our discussion regarding cords. So, could a powercord actually be acting as a filter? If so, that explains why one might hear a difference with one piece of equipment, but not another. Maybe powercords act as a filter that takes off a bit of edge to musicr by killing high frequency noise in the mains power to some degree. Who knows?
Summary: Improvement, or lack thereof, may be dependent upon the equipment's power supply implementation.