I would not feel comfortable feeding layer diet to a rapidly growing bird. The calcium

hosphorus ratio in layer food doesn't develop bones properly, so there can be both poor growth and long term skeletal issues, decreased elasticity of the tendons and ligaments, sometimes abnormal organ development due to microscopic soft tissue mineralization, plus the protein levels are less than ideal. It might not be a big deal for some people if their chicks grow a little slower, and it just takes a few more weeks to get to slaughter weight (although that's a lot of wasted food, which is expensive). But it's a huge deal if you're breeding purebreds, with the intention of raising long-lived and healthy breeding stock, or if you're raising birds for pets. Chick food is fine to feed to the broody, as she's not laying eggs while the chicks are really young. For flocks with both chicks, broodies, layers, and roosters all mixed together, an excellent solution is to feed either a chick diet or a general flockraiser diet, which are typically 18-20% protein and no excessive calcium, but also provide oyster shells for the laying hens. Typically the layers crave the oyster shells, and the chicks and rooster don't, so everyone gets what they need nutritionally.
All the bags of layer diet that I've ever seen, regardless of brand, all warn to not feed to birds under 18 weeks old.