it would fill up with water and slosh around, no drain that I recall. I think its a bad idea because i normally keep dock line, antifreeze, spare plugs, spare shirt, a small towel, assorted tools in the bottom of my dry storage bin, on top of that is my soft sided cooelr.
my old yami used to have a foam "cooler" with a drain into the bilge, but I rarely used it, it was in a bad spot.
What I use is this.... with a couple of ice packs and one water bottle completely frozen. I hydrate a LOT when riding over the course of a 4 hour ride, 4-6 water bottles + either diet coke/lemonade/tea/coors light.
this works fine, I keep some cash, ID, and some chips or beef jerkey in the side pocket, two ice packs (the blue things) in the bottom, several bottles of whatever, then a turkey sammich on top.