I see where you are coming from, but you are thinking "too small".. Think about the entire upper surface of the car..it is kinda cambered like the upper surface of a wing right. This is why we "float" at high speed, the Car is itself a wing...low pressure on top, high pressure on bottom. As far as the cowl area goes...alot of people think it is a high pressure area, but it is relative. The pressure at the cowl is higher than the pressure at say the hatch vent..which is why flow thru venting works, but it is lower than the pressure in the engine bay....remember, the faster the air is moving, the lower the pressure. Now having said that, there is turb at the cowl, but right at the windshield base.
Now in keeping with the aero theme, why does an airdam keep us from floating at high speed? It depends on the type of dam...the BRE type worked mostly on the drag principle. It created drag at the lower cowl that helped to "hold" the nose down. The larger "dam" types work on two principles. Drag and Vacuum. There is a little drag created by having the dam, and if the car is set-up low enough...a little bit of vacuum right under the nose...dont ask me exactly how it works, A F1 or Indy car engineer could explain it better.