I doubt anyone would disagree that a parachute is not a dry fly imitating a sub-imago. If the parachute hackle is suspending the fly; and the fly body is beneath the parachute; the body is obviously at least partially submerged and taken probably as an emergent insect.
Unlike the caddis, however, the sub-imago duns ARE a big source of food for trout during a hatch. The fact that they have to float along while waiting for their wings to dry off in order to fly away makes them a good target for the fish and a good pattern for the fisher.