[Theory] Octave pedal with phase shift (inversion)?

Hello!

I have a somewhat theoretical question regarding octave pedals.
Let's assume a nearly perfect pitch shifting algorithm that accurately divides all frequencies by 2 without introducing distortion or other artifacts.
Now, when blending the octave-down signal with the direct/dry signal (externally), would it make a difference whether or not the octave-down signal is inverted or not (phase shift 180°)?
I don't have one yet to test this in practice...