I keep my open. It doesn't make any difference on how dirty the motor gets when it is off or on. All of the air comes in through the front of the truck, through the radiator area, a little more area doesn't make a difference. Probably helps when the truck is sitting still, the heat can rise out of the hood scoop.
My motor stays clean, even with the hood scoop open. I clean it about every six months. Even if I shut the hood scoop, I would still need to clean it in about six months. It is kind of like if you had the garage door wide open, and someone was trying to put sealer around the light bulb area because air might come in through that area. The radiator area is wide open and that is where the air comes in at.