power cables - not in the signal path?

According to popular wisdom the AC power is not in the signal path and therefore a power cord, AC conditioner or similar should have zero audible effect.

In a don quixotesque attempt I'd like to turn this perception around: the AC is 100% in the signal path - more so that the actual low-level signal that gets amplified, and I think I found the simple words to clarify this.

The low-level signal is actually only modulating the high-voltage (high-intensity) signal produced by the transformer. Those electrons from the transformer are the actual electrons we "hear". The low-level signal is simply lost in translation. In a simple example, a 0.1V peak-to-peak sine signal gets amplified (say) 10x by a 10 V continuous (transformed) DC. The output is (say) a 1V sinusoid oscillating back and forth in time. If the 10V continuous is NOT actually exactly 10V (but is actually has noise) - then the noise will directly reappear "riding" on the 1V output.

Hence the need to keep the AC noise-free.

(Of course I purposefully neglected for simplicity the other effects (need for instantaneous delivery of power, etc..) for which I did not find a simple enough description (without reference to I/V curves and impedance / capacitance details, that is).

Does is make sense?

Thanks
C.