The question boils down to this: if you had the ability to measure power consumption of white noise (equal amplitude across the audible spectrum, not necessarily 20Hz to 20kHz, if you could do it for 50Hz to 10kHz that would be a sufficient demonstration) by the two halves of a bi-amped speaker, what would you see?
Since the crossover point between the low frequency section and the mid/hi frequency section of a speaker will almost always be in the lower part of the 50 Hz to 10 kHz range, most of the energy of white noise occurs at frequencies that would be above the crossover point. So most of the energy of white noise would be delivered to and reproduced by the mid/hi section of the speaker. The spectral composition of music is very different, of course.
With music, per my earlier comment, if the crossover point of the speaker is 350 Hz both amps would typically have to supply approximately equal amounts of power. If the crossover point is significantly less than 350 Hz the high frequency amp would typically have to supply more power than the low frequency amp. If the crossover point is significantly higher than 350 Hz the low frequency amp would typically have to supply more power than the high frequency amp.
With music this relationship will of course vary somewhat from recording to recording and from moment to moment. Which is why I used the word "typically," meaning that it would hold true the majority of the time.
Regards,
-- Al
