I have to ask why you are doing it and what is the intended end result? What process? The only reason I have used somethng like that is when I have tried to clean up a dirty recording, maybe attempting to clarify a vocal or reduce bass rumble etc. or trying to manufacture a streo effect out of a mono track by duplicating but in that case any effects I add would have to be on both and that could be risky.
If you are doing the above then duplicate your tracks with no FX, export them (stereo interleaved) then reimport as a stereo track and then apply (panned) FX.
If dealing with audio then the sample won’t have (shouldn’t have) moved but the effect, particularly reverb or delay, will “duplicate” the track again and the phase you hear is likely in the effect and not the actual track (against the other original track). Mute the effect and you will / should get nulling.
All that I can say is it’s working fine. I can’t help thinking this is a theoretical issue. Most of my projects contain parallel processing without any perceivable unwanted artefacts.
Q: What do you do if there’s a drummer at your door?
A: Pay him for the pizza!
Q: What do you call a drummer who’s had an argument with his parents?
A: Homeless
Q: What did the drummer get on his IQ test?
A: Drool 
I thank you!
badoom tsssh!
Same here!
Heavily relying on parallel processing and never had any unwanted effects. Even when the parallel channel contains a bucket load of 3rd party VST’s, the delay compensation handles it correctly and the combined signal doesn’t show any (noticeable) phase problems.