Catalina 30 icebox drain
My '92 Catalina 30 had the icebox drain hose connected to a foot pump which was then routed to the sink drain. The advantage was you could let ice water build up in the bottom of ice box to help chill beer. The disadvantage was it wouldn't drain passively so you had to remember to take all the left over ice out and pump the thing dry before leaving the boat. The only reason I can think of for not simply running the drain hose directly to a 't' on the sink drain hose would be the relative level of the two drains. It might be possible to get sea water back up into the icebox when the boat was heeled way over. You could prevent that, of course, with a check valve.