I have read in a few places that undertrays are to stop engine noises escaping, so not aerodynamics just to make car quieter to people outside the car...
I think that's the main reason, although the aerodynamics and fuel economy must come in to it too.
Our other car has them at the rear end too, supposedly all for fuel economy, but they are more permanently fixed and not all flappy like the Honda undertray. All the back end around the suspension and up to the bumper is all faired in, like the engine bay. In fact, the engine bay undertray is solidly fixed, with only a drop down flap for access to the sump plug. The oil filter is accessed through the wheelarch, you have to take the damn wheel off!