I turned that compartment into a livewell with a recirculating pump. I placed the drain in the starboard back corner, thru a piece of hose, and out of the console to the deck by a thru hull on the side of the console. There is not a lot of "fall" in the hose, so it drains slowly in the end. I don´t mind as I usually drain it at the end of the day, when the boat is going to bed......
I don´t think it will serve as a cooler as it is not adequately insulated. Ice won´t last very long unless you fill the space around it with some kind of foam......