From an aerodynamic perspective, the air dam on the leading edge of the bumper is the most efficient at reducing drag and increasing downforce.
The reason the stock air dam is needed is because the path of least resistance on the stock setup would be underneath the radiator. The trade off is that you increase drag and front end lift, which is not desirable. In fact, I would argue that there is no reason to go to a larger air dam in the stock location unless you are having cooling issues.
By boxing the radiator in, you force the air flowing through the grille opening to flow through the radiator. Depending on your cooling system and power plant, you may need more cooling which would be best accomplished by increasing the size of your grille opening. For a track car, you want the opening as small as possible for the purposes of drag reduction and increased downforce, but still large enough to provide adequate cooling. This is the reason why people tape up their grilles, as tape is easily added or removed for changing weather conditions. A cold day means more tape, a hot day means less.
If you have the leading edge air dam (provided it is low enough to be effective) then having a second air dam behind it will do nothing but add weight. Additionally, having the air dam low reduces the amount of air underneath the car, which by default creates lower pressure behind the air dam through which the higher pressure engine bay air will escape and travel underneath the car. With a boxed in radiator, the air must travel through the radiator to enter the engine bay, where it will then exhaust underneath the car.
If you are having cooling issues with your boxed in radiator, I would submit that you either need more grille opening, or simply a better (as in, larger, higher volume, more efficient, or all of these things) cooling system.