The icebox drains into the shower sump, which is the small box that is visible under the floorboard hatch in front of the main table. This in turn is pumped out thru an above-the-waterline thru-hull via a pump that is activated by the manual switch in the head/shower area. The thru-hull is located on the stbd forward area, accessible from the V-berth. In the original installation, it had a gate valve installed there.
When the shower sump fills up, water starts to back up into the icebox and the floor drain of the shower, under the teak grate.
Some 323s have had the sump box removed, and allow the icebox and the shower to drain directly into the bilge. This is a bad idea, as all the organic debris from the inevitable icebox spills, plus the shower and small sink output will quickly have the bilge smelling like an open sewer, especially in the hot summer months.