What would actually be normal is for the water to drain to the stern (where your ice is built up) and then drain in toward the bilge (center of the boat). I wouldn't expect drain holes in the floor - but I would expect that where the locker meets the deck there is a space that water can make it through.
It would make sense that the boat would collect water on one side of the deck if it's not level, because inside the goal is to flow to the stern, down the centerline of the boat into the bilge.
That said - how ya' gettin' all the water inside in the first place? Is it a one time thing, or are you regularly gettin' the deck flooded? Even with dogs and kids getting in and out of the water for an afternoon, I don't collect quite that much water.