The cooling advantages of the undertray are easily apparent. Look underneath the car at the radiator. The bottom of the radiator is angled back and there is a large hole between the radiator and the front lip/bumper. When your car is moving it forces air through the front lip. The direct path for the incoming air is to the engine bay. However, when air is forced into the engine bay there is a resistance from when the air hits the engine. Without the undertray, air will take the path of least resistance and lower pressure and go underneath the car before ever hitting the radiator. Thus the undertray is a critical component of ever FCs cooling system.
The aero improvement with the understray is 0.01CD better than a car without the undertray. The reason is quiet simple, the flow under the car is improved by having a smooth passage.