From my experience, between 2 and 4:30 in the morning the ships decks get pretty empty as more passengers are asleep and the crew is cleaning. You may not be able to find a private place but you can make it happen; just not for very long.
I actually thing Royal Caribbean ships have more places where you can "get lost" than do Carnival ships. Carnival ships are pretty boring when it comes to layouts. Royal Caribbean ships have a much more inviting and well thought out approach with bars and clubs in places that you may only stumble upon by accident.