I think guests have no idea how many of these end up in the incinerator room. (As crew members on board we're responsible for bringing our own trash to sort out and there are always buckets of these getting processed.)
It's an unspoken secret that Crew Members may be able to sneak and keep them on their own to avoid their fate in the trash, but when these are found by crew in public areas the USPH policy onboard is to dispose/offload them for recycling after the cruise (without letting guests know). *Edited to add that obviously like any job there are people who will care more than others, and managers who are more strict about it and other departments who aren't. But if the ship is about to undergo a USPH inspection soon you can bet that anything left around that cruise gets removed so they don't get dinged/points off*
It's a bit of a downer reality to think about that might kill the fun, but imagine if the crew were to just let guests plant random objects in hidden locations on board whenever they wanted and the danger this could present. We do safety drills on a regular basis to locate objects hidden within our spaces for this reason. On the bright side, most crew members are usually not so heartless and if a duck is in their designated work space and hasn't been immediately discovered, they move it to a more conspicuous areas for another guest to take to avoid having to throw it out.
If you ever get a chance, ask the ship's Chief Safety Officer or Environmental Officer what they think about ducks on board and prepare for a lecture!