This would only work if you already had a hen brooding some wooden of infertile eggs and the new arrival was under 24 hours old. In that case, being that chickens are deep sleepers, you could replace the eggs with chicks in the night. But even then you will need to have a brood hat was actually interested in the chicks once they hatch and the entire flock gets on well with each other.
As for the mothering and nourishment, all a hen really does is keep the chicks warm and protect them from the other hens and rooster. You will do a far better job of this with a 3 week old chick that a hen will.
I add new hens to the flock when they are pullets. I leave them out into the portable run for a few days so the other free ranging hens can see them them. Then I put them (usually asleep) on the roost well after the other hens are sleeping and make sure I am out there at sunrise to open the coop. The idea is the eh hens smell and hear the new arrivals while they are docile.
It has worked for three years, sometimes with some hen drama but so far without blood shed.