For what its worth, draining the icebox directly into the bilge, although commonly done, is probably not such a great idea. All of the inevitable food spills and leaks in the icebox will result in an organic "sludge" building up in the bilge, causing anything from a mild "boat funk" smell to a full-on open sewer experience.
The early OEM configuration had the icebox draining into the shower sump tank, which gets pumped overboard later by its own purge pump. I believe later designs went to pumping the icebox directly overboard.