The stock Quickie and the Quicksand both include the power supply (batteries!) in the signal current loop, so the power supply imperfections do have an opportunity to impact the sound. The PJCCS substantially reduces that effect. Adding long lines between the power supply and the circuit offers another opportunity for imperfections to affect the sound. One way to change the equations is to put a capacitor across the power supply and inside the amp circuit, which lets the cap take most of the signal current, at least at frequencies where its impedance is less than that of the cable+power supply. Whether that's an improvement or not remains an open question.
So much for theory. Experimentation is the only way to find out.