On phase cancellation
This is a discussion of phase and phase cancellation as it applies to guitar rigs.
Let's begin with a definition of terms to be sure that we're all on the same page. "Phase" describes the angular relationship between a signal measured at two points in a system at a specific frequency. (This is "relative phase"; it has nothing to do with whether the speaker moves in or out on the note attack...)
In a guitar amp, nearly every bit of the circuit introduces some phase shift. The cathode-bypass caps and interstage coupling caps introduce phase shifts at low frequencies. The bright cap and the presence control introduce phase shifts at high frequencies. The tone stack introduces phase shifts pretty much throughout the full spectrum.
Almost every preamp stage (except for the cathode followers, if any) introduces a phase reversal, which is effectively a broadband shift of 180 degrees.
When people talk about phase cancellation they're referring to the net effects of the phase reversal cancelling the signal. For example, Fender blackface amps with reverb have one more preamp stage on the reverb channel than they do on the bright channel. If you put the same signal through both channels you'll get some cancellation when they get mixed at the input to the power stage. The cancellation is unlikely to be complete because the two paths probably won't have exactly the same phase response across the audio bandwidth. The overall effect will be a thinner sound, much like a phase-reverse switch on a guitar.
You'll notice that, with a phase reversal in the path as described above, the sound will change dramatically as you alter the volume balance right around a certain point. Differences in EQ in either channel will tend to have interesting, if not entirely intuitive, consequences.
My point is that phase reversal isn't necessarily bad in a dual-path situation. Keep your options open. If you have some kind of widget with a phase reversal switch, by all means keep that in your bag of tricks. But don't avoid the mixed-path experiment just because you're not certain about the nominal phase of each path.
Introducing effects in one path and not the other opens up another can of worms. Here the biggest concern is whether you're introducing time delays. By that I don't mean things like a delay/echo unit, but rather the short delays that you get from digital processing. A digital stompbox or rack unit converts your analog guitar signal into the digital domain, does some processing, then converts the processed result back to analog. Each of those steps adds a very small fixed time delay. The total delay in the signal path is normally a few milliseconds.
Now if you delay a signal by a few milliseconds and mix the output of the delay with the direct signal you get what's called a comb filter. This sounds exactly like a flanger running at fixed delay. It tends to impart a certain "hollowness" to the sound. It's not generally what one would want or expect to hear. There really is no fix (at least not one that's tractable by plugging together a bunch of off-the-shelf boxes.)