Many people open the engine cover after a hot lap session at the track (I do it), but it's not really necessary with the NSX unless your cooling system is not working well or you are running a modified engine that puts more heat into the engine compartment (i.e., turbo). The system is well designed and will convect hot air even sitting still. The engine cowl vent serves two purposes: first, it provides an air inlet to introduce cool air into the engine compartment at high speed. It is not a "scoop." Instead, it is an "inlet." The way it works is that the fast air rushing under the engine compartment creates a low pressure zone under the engine. The low pressure under the engine sucks in air from the cowl and draws it over the engine block, exiting under and behind the car. This effect begins to work at about 90 mph, since below that speed the engine isn't running hot enough to need air cooling. You can hear a hiss behind your head as the air is being drawn into the cowl.
Second, the cowl works as a convection vent when the car is sitting still. Hot air from the engine compartment will rise and exit the vent, drawing cool air from the bottom of the car into the engine compartment. Next time you drive the NSX and get it good and warmed up, place your hand over the cowl after you park the car. You will feel the hot air coming out. The design is so effective that Honda ditched the engine bay fan, since it never came on.
Your NSX is well designed from the factory and can manage engine bay heat quite well. There is no need to open the hatch after driving. It is impossible to get the engine hot enough to need it with street driving. At the track, I do it to accelerate the convection cooling of the engine to get ready for another hot lap session, since the engine is running at 8,000 rpm for almost 20 minutes.