There are a lot of experienced chicken keepers who keep their mother hens and babies with the flock. It makes integration so much easier as the mama will protect the babies from the other hens right now. The other hens will learn to leave them alone as they learn flock etiquette. Also, if something happens to the hen (as did mine when the chicks were about 3 weeks old) they will already be accepted by the flock. If you have plenty of room, they should be just fine. With my first batch this year, when I put them together, the boss hen tried to go after my broody and the rooster got between them and protected mama and babies. My chicks are fed in a big black rubber feed pan. They can hop in and out with no problems. They are 2 weeks old and drinking out of the big galvanized waterer with the rest of the flock. This current batch is eating broiler/finisher feed and getting along quite nicely.
Personally, I believe hen-raised chicks are healthier and get along better than brooder-raised chicks.