PJ,
If I understand, even though the cathode bypass cap is out of the output signal loop, it still has an effect on the performance of the output signal loop, namely the output tube?
Back to the OP's original question, with it out of the signal loop, does it matter if the bypass cap is electrolytic or film? And will it still need to be of large value for the low hz?
The power supply and cathode bias circuits are out of the signal current loop at high frequencies. At low frequencies, the parafeed loop is in parallel with another loop, tube - plate choke - power supply - bias RC - back to tube.
The reason for this is that the plate choke inductive impedance at low frequencies is small enough to allow some signal current to flow in this second loop. At the same time, at very low frequencies the "main" loop impedance is increasing because of the parafeed cap. So the signal current gradually diverts to the second loop and away from the first loop.
Anytime there is a nonlinear element in a current loop, it will contribute distortion, so yes, the power supply and cathode bypass caps will have an effect. Whether it is audible (being confined to the lowest frequencies) is more of an open question, answerable only by experimentation.
I should probably mention two other configurations. If the last power supply cap goes from B+ to the cathode (not ground) then it makes the cathode bypass less of a contributor. And, if the parafeed transformer returns to ground rather than the cathode, then the cathode bypass cap is in the signal current loop at all frequencies.
Engineering always involves simplifying the real situation enough that you can optimize it, thus there are always more complications lurking. Definitive answers are never possible, we just learn to settle for "good enough"!
