It looks like the trapped chest does however power the block directly below it (even if the block is an air block, activating devices that are activated by powered blocks around them, like pistons, dispensers, droppers, etcetera.
I've retested, and it appears to only happen when pigmen are shot by ghasts (probably other non-player damage aswell). Also, zombies seem to spawn a lot more frequently as you increase the difficulty setting.
It looks like the trapped chest does however power the block directly below it (even if the block is an air block), activating devices that are activated by powered blocks around them, like pistons, dispensers, droppers, etcetera.