More complicated question than one might think.
Yes is the normal answer.
Pink noise and an RTA program are not hard to come by...I often test for flattest response, also listen for what sounds best...
Guess what I am saying, yes is the textbook answer. The reason...if positive is defined as a positive voltage to that terminal causes movement AWAY from the magnet...think...the diaphragm is behind the magnet, whereas the woofer cone is in front...
So the diaphragm moves rearward and the cone forward, thus are RELATIVELY out of phase. Reversing the polarity fixes this.
But then we are assuming the voice coils in the same plane vertically, but due to horn lengths they often are not.
Newer active xovers, even the el cheapo Behringer, have phase reverse switches, and delay to compensate for coils not aligned.
Factory propaganda-
"SUPER-X PRO CX3400
High-Precision Stereo 2-Way/3-Way/Mono 4-Way Crossover with Limiters, Adjustable Time Delays and CD Horn Correction
Professional stereo 2-way/3-way/mono 4-way crossover featuring state-of-the-art Linkwitz-Riley filters with 24 dB/octave
Individual Limiters on each output for optimal loudspeaker protection
Adjustable time delay for phase alignment between drivers
CD horn equalization for constant directivity horn compensation
Absolutely flat summed amplitude response, zero phase difference
“Low Sum” function provides mono output for subwoofer operation
Individual output Gain controls for all bands
Individual output Mute switches for easy band adjustment
Individual Phase reverse switches for instant phase correction
Switchable 25 Hz Low cut filter on each input for low-frequency driver protection
Servo-balanced and gold-plated XLR connectors for all inputs and outputs
Ultra-high precision potentiometers for ultimate accuracy and repeatability
Illuminated switches for secure operation in dark stage environments
Shielded toroidal mains transformer for minimal noise interference
"
For instance, sound travels 1100 feet per second, or for Rightpondians 340.29 m / s. So if the HF driver is on a longer horn, say a 203 multicell, it will not be "time aligned" with a woofer on the shorter A7 mid bass horn. A very slight delay to the woofer signal fixes this.
HTH, trying to give a somewhat complete answer but fear may be over complicating things...
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