Speckledhen has a hen that when she went broody, she nearly died. I dont know all the details of it, but the chickenS name is Sunny.
She tried repeatedly to break her broodiness I know. She could certainly tell you more.
I am not sure how well they could do without at least water for 21 days. Mine finally started getting up once a day after I put the water and food very near her, and to go poo, but she only did this after the first couple weeks, when i started really worrying about her.
To be perfectly honest, mine went broody in the house, and would only eat high protein stuff, she wanted special things for me to cook for her. lol I was so worried that I actually was cooking for her.
Good luck, she is a gorgeous lil thang!