The open sides and bottom of the nose area will not really hold much air with the car in motion. This area will have lower air pressure directly behind the radiator in front of the side openings in the hood, but this helps to pull air through the radiator (along with the higher pressure in front of the radiator). The area above the HE will be somewhat turbulent with the bottom of the nose left open, thus the reason to have a fan to pull it up through the HE or NACA ducts to blow air down through the HE when the car is moving. Adding a side scoops to force more air into and out this area may help reduce the turbulent air to make some it crossflow. To refine your idea, and this is just my thinking out loud, making the side pieces both scoops will force more air into the area and force the air to flow mostly out of the bottom of the open nose. Conversely making both side piece as air extractors will create a higher vacuum in the area which will try to pull air from under the open nose, but also make most air flow out of the side openings in the hood. Again, with the open bottom under the nose, different speeds will enhance or hurt either of these solutions.