Well, that's the funny thing... The phase of the signal actually flips with each gain stage (in a normal plate-fed stage). That's why you can jumper the channels in some Fender amps because they have the same number of gain stages in both channels and you can't in other Fender amps because they have a different gain stage count and thus are out of phase with each other. and if the phase of the input power changed, they would both change as well and still be out of phase, so...................
And then there's the constant phase of the input signal (guitar) which could be affected by phasing with harmonics of the 60Hz cycle on the US grid (50Hz in Europe and other areas).
Ever play through an old amp where it had a ground switch on the back? The ground switch was designed so you can flip the ground connection so you don't get electrocuted when you touch the mic if that's grounded differently, but that was rendered necessary by the third ground prong. Flipping that switch can make things sound subtly different if you A/B the amp in both positions while playing. It's mega subtle, but it could be the smoothness/roundness the OP describes.
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