Nah I don't think so.I find it so hard to believe that a broody duck would hold her poop while on the nest. They sure as heck can’t hold it any other time. And just so you know, broody poop (from a chicken) is the biggest and the stinkiest poop ever!
I guess the squeaky clean comes from the duck washing the eggs with the water from her feathers.
I really think when they decide they wanna sit they just don't soil where they sleep.
Now they might track poo in on their webs if they step in it.
Or another duck might defile the nest. Kinda depends on their set up.