Both Layer and Grower should be about 16% protein. There is no protein difference in Layer and Grower. The only significant difference is Calcium. Layer has a lot more calcium than Grower. Calcium is what will do the damage.
Actually, you'll see a product called Developer on the market. This is a 15% protein feed that is good for them from 13 weeks until they start to lay. The slightly lower protein feed slows their body growth a bit so their skeleton and internal organs can develop better relative to body growth. But you can feed 20% protein combined Starter/Grower from day 1 until they start to lay. The exact amount of protein is not that important as long as you don't go to extremes either way.
Will feeding Layer to 4 month olds hurt them? Probably not, but I'm not sure. There are plenty of studies that show that feeding Layer to chicks can seriously hurt them. Mortality rate is higher and when they look at the chicks internal organs in those studies, they find nasty growths on the liver and kidneys. Not all chicks have significant damage, but a whole lot do. Not all of it is evident without opening them up to look.
My problem is that all these studies start with one day old chicks eating Layer for all their lives. I don't know of any studies where they started the chicks on Starter or Grower, then at 6 weeks, 10 weeks, or 16 weeks switched to Layer. I don't know where the age cut-off to where the calcium in the Layer causes damage is. Also, it is not purely the percent of calcium in the feed that counts, but how much total calcium they eat in a day. If they are free ranging or eating a lot of things other than the Layer, they are not eating as much total calcium so it is not as likely to harm them.
It is not an instantaneous effect either. It won't hurt them to eat a bite or two of Layer. The damage is more long-term. It is the steady diet that counts, not a one day thing.
So I'll say it probably won't hurt them at that age for them to eat Layer, but I really don't know. I feed Grower with oyster shell on the side when I have a mixed age flock. I've also fed 20% Flock Raiser when I could not get the Grower. You really don't have to be that precise with protein.