That is my understanding, yes.

The reason they're so efficient is that the output transistors are always fully on (lots of current, little voltage through/over the transistors) or fully off (no current, high voltage) which makes the UxI losses low.

Switch the transistors fast enough and the speaker has no chance to follow the actual signal, but only the averages. But to accurately reproduce higher notes you have to switch very fast, which is the reason fullrange D or T class amps are rare; mainly they're meant for subs.

Hmm, looking at some links it appears that at least some have an inductor/cap filter at the output (to which the speaker probably adds a fair bit considering its inductance) to help smooth the signal.

Good tech paper, and another one.

/Michael