what i meant by the center cutout is something like this
or this
this is the 2010 bluemotion so it should have the best aero this this generation
even cars without an undertray sometimes have an "airdam" that's lower at the sides that in the center.
this is mainly to deflect air away from the front wheels, but also to allow more air under the car. also notice the curve of the bumper, it seems as if all air that can't be felected sideways is allowed under the car in this area
one reference i read to this was in the aero developement on the opel calibra with a 0.26Cd where it was found raising the center of the bumper lowered the Cd, but this car also had an undertray.
this can be a bit confusing as there's also reports of big airdams reducing drag, so ultimately it'll depend on getting the size right for your car, but if you can make the bottom of the car a bit more aerodynamic with a small undertray under the bumper and perhaps the engine this could make a difference.
an undertray also makes the car more quite and keeps the engine clean, so nothing but advantages.
perhaps it's also interesting to note the small dams the mercedes in the top picture has in front of the tires. these are quite common in current cars and are said to help stability and aerodynaimcs... gains aren't huge, but a difference can be felt, and they're really easy to make. but getting the size right is a different matter. and oversizing kan kill fe
from observations on production cars it seems a safe dimention for a non lowered car is to leave them 1/6th of the total wheel hight above the ground.
this is a rough avarage of what i've measured on different cars.
on production cars they often only cover the inner half of the tire (perhaps as this is also the with covered by the bumper), but sometimes extend past the tire inward to shield the suspention and inner wheel well.
but perhaps i digress from the original subject to far here