Not unless the slope of the cutoffs for both are the same.Not true. One can achieve near perfect integration with a main 1st and 3rd order sub with polarity inverted.
Slopes must be adjustable. Ideally on both the main and the sub. They do not have to match.
Subwoofer phase adjustments are simply (very small) timing delays applied to ONE of two speakers attempting to producing the SAME frequencies.Not unless phase adjustment is done with a delay or by physically moving the speaker.
Lastly, one cannot "invert the phase." This makes no sense. Adjusting the phase 90 degrees, 180 or 270 of a subwoofer is adding a small delay in the timing of the sound wave. There is no way to do the opposite and speed the sound wave up, hence no such thing as, "inverted phase."A typical phase control does not add delay. It shifts the phase relationship in the speaker range. If one inverts polarity, the phase shifts. The timing remains the same.