They do not poop when broody, they keep the nest pretty darn tidy, but they have been observed drooling/spitting on the eggs in certain instances to boost humidity...
On the humidity subject, broody birds have little control over humidity and thus don't really monitor it as there is little they can do to control it... If it's 95° and rainy with 100% humidity that is what it is, and if it's 95° with 30% humidity that is again what it is, less them drooling or spitting on the eggs, as they lack sweat glands and can only marginally raise humidity with their skin to egg contact...