My hens have food and water in the coop, but I still pick up my "broody Ethel" twice a day and carry her outside. She runs around, eats, scratches, and then heads back in for nest duty. We are moving into week 3, and she has lost a little weight, not too bad yet. Today she actually got up and went out on her own! Yay Ethel!!
I have a broody Ethel too. She won't eat while setting even if she does get up to drink and poop. I put all her favorite things in a dish right next to her, she didn't even have to stretch her neck to eat it, but she wouldn't touch any of it.
She lost considerable weight, and after the chicks hatched, I made the decision to take the chicks away and put in a brooder so she could gain her weight and strength back. She had to stay in the broody pen alone for about 3 weeks until l thought she would be strong enough to defend herself in general population again. She has done fine though.
They supposedly will get off the nest once or twice a day and eat, drink and poop. I haven't had one that refused to do this, but then I've only had a few actually hatch chicks. I did have one that lost a lot of weight, I have read it is normal for them to lose some, but she did get up at least once a day and do all three, I know, because she would run from me when I went in the coop (flighty little thing that she was.)
She will get off and eat but you won't see it. I thought my broody wasn't eating, but I started watching the food level. And it was disappearing. She was "sneaking" it, protecting her nest. I only caught her eating a couple times in the time she was sitting. So don't worry.
ETA: Good luck with the broody poo, that stuff is the NASTIEST, most FOWL thing I have ever had the extreme displeasure to smell. It even beats dog barf.