The turkeys will be getting less protein than they need. The good news is that they will not die. However, they will have to eat more food than usual in order to get the required amount of protein that they need. They also won't grow as fast as they would have with enough protein.
There is one possible advantage to this---Your poults won't be growing quite as fast, so they likely will not "outgrow their internal organs". By this, I mean that the commercial turkeys of today grow so fast that their hearts, lungs, livers, etc. cannot keep up, and the mortality rate is quite high on these birds, especially when they get older.
If you have "heritage" turkeys, you won't have to worry about them outgrowing their organs.
You should be just fine with feeding the layer mash.