...does the power usage scale with the volume and demands of the speaker?Yes, absolutely, in the case of class AB, and even more so in the case of class D. For class A, though, the AC power drawn from the wall outlet will be determined by the amplifier and will be essentially the same all the time, with the power that may be supplied to the speakers at any instant subtracting from the power that is dissipated (converted to heat) in the amp. (But as stated above almost all of the power supplied to the speakers will then be converted to heat in the speakers).
Also, keep in mind that most of the time under most circumstances just a small fraction of the amp’s power capability will be utilized. Brief dynamic peaks in the music will typically result in much more power being delivered to the speakers than the time-averaged amount of power that is delivered. Although different recordings can differ greatly in that regard. Recordings that are dynamically compressed to a severe degree (which is particularly common among pop and rock recordings) may have less than a 10:1 peak to average ratio of the amount of power delivered to the speakers, while there are some classical symphonic recordings having minimal or no compression for which that ratio may be more than 1,000:1. In the latter case very little power will be supplied to the speakers, on average, and hence a class AB or class D amp will not generate much more heat than when idling.
Regards,
-- Al