Unless we are taking about race cars with aero, You will typically have high pressure behind the radiator, it is hard for air to escape under the car. The air backs up in the engine compartment. Without somewhere for the air to go like a hood vent, you could make the problem worse by making a very long undertray.
I don't know what you were trying to say about your fan. If it is on all the time, yea that is bad and stalling airflow through the radiator.
I have a Setrab series 6 34 row oil cooler. The core is 11.25x10.25. I have no ducting to it at all, it is just sitting in front of the radiator with a 2 inch air gap between them. I probably need a duct on it with a splitter to get air up to the top of the cooler. It should be cooling a bit better that it is.
I run a Howe dual pass radiator in my car with a Spal dual fan and shroud.