I'm sure that this matter is more involved than I understand, so I will be interested in hearing more about it.
No I’m sure it’s far less complicated than you’re trying to make it. It’s the same thing ecc83 talked about above. Flipping polarity
might help with gain before feedback, but only kind of accidentally, probably only at certain frequencies, and definitely only until you move either the guitar or the amp.
I read a thing a while back where Brian May talked about using his pickup phase switches in a kind of interesting way. Now, if you’re playing through just one pickup, the absolute polarity is pretty much arbitrary and doesn’t matter. Flip it one way, record, flip it the other way, record, compare the two, hear no meaningful difference. BUT if you’re playing in front of a loud amp, and you hit a note and hold it and it goes off into that self-oscillating feedback thing, and you flip the switch, it might just cause the held note to break to a harmonic. The harmonic mode of an eBow is very similar. The driver is opposite polarity to the sensing coil, so it is kind of driving against itself, which magically causes the first harmonic to jump out.
Now, if you happen to be pushing an asymmetrical waveform into an asymmetrical limit, the polarity of the input does make some difference. If the higher side of the wave goes one way, it hits the limit sooner than if it goes the other way. It’ll be noticeably more distorted. But if the limits are symmetrical, then it doesn’t matter, and if it’s not hitting the limit in either direction anyway, then it doesn’t matter and won’t be audibly different either.
But yes sometimes polarity matters between different sources. A kick drum and a bass, or even a bass guitar and a guitar might work better together one way or the other. It’s pretty much accidental again, and if there’s any amount of timing slop, it could be different for each hit, but bass waves are long enough that it could be a matter of degree rather than full reversal from note to note.