Changing the relative phase between the woofer and tweeter will of course alter the summed power response, as well as the vertical dispersion charasteristics, of the complete speaker.
But I think it's clear that the relative phase between the two drivers has been preserved the whole time . . . what's still unclear to me is whether the relative phase between the drivers and the passive crossover has been changed, or simply the relative phase between the loudspeaker and amplifier. And I'm also not sure under which conditions absolute phase has been preserved or altered . . . so it's difficult to make further speculation.
But I think it's clear that the relative phase between the two drivers has been preserved the whole time . . . what's still unclear to me is whether the relative phase between the drivers and the passive crossover has been changed, or simply the relative phase between the loudspeaker and amplifier. And I'm also not sure under which conditions absolute phase has been preserved or altered . . . so it's difficult to make further speculation.