My concern with adding chicks is the level of calcium in Layer feed. Studies have shown that sometimes the excess calcium can harm them. I always have non-laying chickens in the flock, a rooster, chicks, maybe a broody, and maybe molting hens. So mine never get Layer but I always have oyster shell on the side for those that need it.
I suggest you look for a feed available to you that has the protein content you want and a calcium content of around 1%. Layer is going to have around 4% calcium, too high. To me the name (Chick Starter, Grower, All-Flock, Flock Raiser, or something else) is not important as long as the nutrient analysis is what you want.