Well, bias of course affects distortion performance, and I have seen many, many amplifiers where the final quescient bias level when warmed up varies with how much load there is on the amplifier when its warming up, and ends up being very different from the value and conditions specified by the manufacturer in the biasing procedure. These thermal subtleties seem to be lost on a great many engineers, and a manufacturer's audiophile "brand reputation" seems to have very little correlation with competency in this area.
As far as offset goes, most modern amps *shouldn't* exhibit a change in distortion performance as a result of an offset adjustment. But many early solid-state designs, including the GAS amps, don't have a current-mirror on the input diff-amp, which means that the balance of quescient current between the diff-amp pair is highly dependent on component tolerances . . . and offset adjustment. And even-order distortion products rise pretty quickly as the diff-amp becomes unbalanced.
With a distortion analyzer, oscilloscope, and a bit of experience, one can easily see the different effects of different distortion mechanisms on the amplifier as a whole. But without this, you're pretty much just "stirring the soup" of whatever flaws the amplifier has, and getting whatever floats to the top.