Honestly you're overthinking this. The car is not that sensitive to airflow at least something as small as that inlet, this isn't a full fledged race car or F1 car. The air entering the engine bay would likely slam into the engine/everything and disperse around. At that point as pointed our above you're just introducing more air and essentially creating drag. You could try to create an exit somewhere, but that doesn't mean the airflow is there. Proper race cars are ducted for this very reason. The air inlet runs off of the high pressure from the front of the car providing a wall and the resulting engine intake providing negative pressure (the turbo pulls in air).
Here's what you'd really want with that idea. There is an inlet in the bumper to the
radiator . Both the lower opening and the twin openings in the center.
The inlet passes air over the
radiator fins to provide thermal dissipation and then a duct/ramp behind the
radiator creates a path for the hot, energized (and expanding) air to diffuse into. This path ultimately exits via a vent through the hood.
(Not an Integra, but here's an example of proper ducting)
Here's the hood vent. Notice it's kinda forward, as there's only so much room to before you run into the
engine block.
This is over-simplified however you get the idea.