Oh they do.
We decided to move a broody hen from the very inappropriate place she had decided to sit and my daughter volunteered to move her. I am very glad it was her rather than me......nasty mom!
She picked up said broody who farted and pooped continuously for the time taken to move her to her new resting place.
As she had not been up and about for 2 days, the gas propelled broody poop managed to cover all one side of her sweat shirt , jeans and wellies. I really should have taken a picture but I was laughing too much.....nasty, nasty mum.
Still it's usually me who gets the chicken poo, lamb poo,bitten fingers, head butting, foot trampling etc.that is inherent with chickens, sheep, and many other animals.