@Pickychicks I brood with deep litter runs so I am not sure what your concern is. Chicks will and should follow mom as soon as hatched and fluffed and mom leaves the nest at day 2 or so. They scratch, peck, and act like little chickens running around in their down coats using momma for a warming hutch when needed even in my cold wet as long as they are out of direct weather. Baby chickens are not like baby birds that stay in the nest while mom flies away to bring back food. They follow her everywhere. It's hysterical to see mom pick up her skirts and the sea of legs under her all skitter together.
I've main cooped hatched in a back corner just fine. I don't deep litter in the coop, but that wouldn't be a problem for the hen or chicks. As long as mom and chicks can safely get to food and water and back, they will be fine.
More concern is to mark set eggs, set at the same time, making sure hen is truly dedicated by showing 2 days of constant setting on that spot meaning only 20 minutes or so off per day. You don't want other hens laying in her nest and mixing eggs up or pushing momma off the nest.
There is an Old Fashioned Broody thread here on BYC you should check out too.
LofMc