Some may purr a little while on the nest...but when they get down from that nest, I would call it anything but "singing". More like announcing at the top of her lungs that she is all alone, the flock are out ranging and she wants to relocate them by calling to them....loudly...and raucously.
I imagine the words are something like this: "Hey! Hey! Hey! You guys!!!! Where did you go???!!!! I'm here! I'm here! I'm here! Can you HEAR ME????"
I wouldn't call it singing lol more like a screaming bok bok my hens do it every time they lay an egg and the other hens usual join in and even my roo will make some noise its kinda like there making an announcement that they have laid an egg and everyone needs to know.