Does AC Power Cord to Linear Power Supply matter?

I should add to my previous comment, that hearing the negative effects on SQ of noise on your AC line (most often generated in your own house or by your own audio gear) is only likely if your system is already capable of high resolution. Owners of lesser systems may not notice a difference.

In addition to high frequency noise produced by LPS there is 120Hz component very difficult to filter out. In addition LPS in amplifiers is almost always unregulated (line and load). Recently quiet switchers operating at much higher frequencies appeared. Rowland used them in Capri preamp (no other reason than noise reduction) and recent top of the line class AB amplifiers (operating at 1MHz). My Benchmark DAC1 has linear power supply inside but the newest version DAC2 has internal switcher to reduce noise by another 10dB. Modern switchers operate/switch at zero voltage/zero current while LPS switches when voltage is the highest. Rectifier diodes are most of the time too slow to react conducting for a moment in opposite direction causing voltage spikes.

Of course not.