Class D amps are always operating at the limits of their power supply and their output devices any time they're on, so "extra" demands on the output stage like normal playing transients are either met by increased wall current consumption to supply the needed power or the power supply will simply hold output at maximum, but the transient will not be reproduced. A few expensive PA type class D power amps have dual supply rails for this reason and more robust output transistors to give them the extra "oomph" of a class A/B amp. They also don't weigh much less than a conventional A/B amp. Their only benefit is more efficient operation at low volume.
There is no "peak" power like in an class A/B amp, where the inductive potential of the power transformer and the main power supply filter caps act as a reservoir, storing "unused" supply current until a transient expends it. The recharge rate is the frequency of the wall current, 60Hz in the US and 50Hz most elsewhere. While switching supply amps have a much faster recharge rate, up in the radio frequency range, their inherently much smaller power transformers and filter cap banks give them a much less amount of stored power, which is why a quality class A/B amp can outperform switching amps rated at twice its power, even before wall current is taken into account.
