It's not an issue with the performance of a single channel so much. With a fixed frequency PWM amp with synchronized multiple channels (i.e., same reference oscillator), you don't get heterodyne artifacts at the difference frequencies (well, that is, the difference freq. is zero, a.k.a. d.c., so there can be offset voltage generation)---that's one of the appeals of such.
With a multiple-channel variable-frequency amp system you can get audible artifacts, and they manifest usually as whistlers or birdies at ~zero signal. If a given pair of amps is offset at the zero-signal frequency by a few kilohertz (region of high aural acuity), it can be heard deep into the noise floor. So even if it measures well, it can be audible if you are listening for it. And potentially embarrassing.
Now most of the time the music overwhelms this sort of thing, so if you are synchronized at zero signal there is not often much of an audible problem. The other approach is to intentionally offset each amp from the other by, say, thirty-forty kilohertz. With that strategy at least you won't hear birdies at quiescence.
And if you isolate power supplies, and lowpass-filter inputs adequately, and use input devices with low rectification propensities (like JFETs), you may not have much of anything to worry about.