To ask a stupid question (maybe not so stupid since I actually served in the Navy onboard a Navy ship and spent a fair amount of time at sea) - couldn't they just use the bathroom over the side?
I suppose in theory you could, but anything besides a male #1 would be entirely impractical and unimaginable given all those people onboard. The way you wrote your question is awkward. I can certainly imagine throwing waste overboard if that's what you mean.