Will probably work better that way, if you can keep the cover on the cooler when it is pressurized. The important fan characteristics are CFM vs Back Pressure, usually shown as a graph on their data sheet. You can measure the pressure difference of your present setup with a homemade water differential pressure gauge like this one. Made of clear plastic tubing with water in it. Stick one end in your Cooler box and the other end exposed to free air. It's convenient beacuse fan back pressure is measured in inches of water.