Switching polarity of tweeter in two-way design

Not really. That will only work if the crossover frequency's wavelength is exactly twice the distance between the tweeter and midwoofer. And it would only work at that one frequency.

The tweeter is wired 'backwards' not to time-align anything but to 'offset' the response spike that occurs in most 2-ways if the tweeter is not reverse-wired. I don't pretend to understand it, but the result is to NONtime-align the system.
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Agree with Jbehr. I always figured the reason for putting the tweeter out of phase was to cancel its response overlap with the woofer. Time aligned designs usually have some slant or tilt thing happening to place the tweeter farther away than the woofer.

I have seen frequency response plots of two way speaker systems with the tweeter hooked up each way. One shows a dramatic downward spike at crossover. Almost complete cancellation. In fact, this is the best way to determine the exact crossover frequency.

However, this effect is probably seen because the microphone is located at a small fixed spot in space, so that the distance to the two drivers is fixed. For real-world listening, polarity of the tweeter does not seem to make a lot of difference. Best idea is to try it both ways.