Either way, it's the same low protein, about 8%. If you feed too much corn, period, it lowers the overall daily protein content of their feed. Layers need at least 16% and preferably 18-22% protein for optimal health. Chicks need minimum 18%-24%. Any corn they eat must be averaged into their daily protein. If you fed 1/2 corn and 1/2 layer feed that is 16%, you'd get an average protein level of only 12%; that is, if they ate exactly the same amount of each. Mine would eat most all corn if I gave it to them in their feeder so they don't get even my better-than-plain-corn 13 way scratch mix in there, only the layer pellets.
The exception would be if I had adult roosters with no hens, which has happened in the past. They can eat that 13-grain mix, which also contains its own grit and is 16% by itself. And there are differences in birds who have free range over rich pasture as opposed to those penned 24/7.