I'm on the fence about this... Most people would probably say that you should provide supplemental protein but a part of me wonders if we really need to be that scientific about our birds' diets. After all, most of us don't calculate the exact percentage of proteins vs. carbs vs. fats in our own diets. And, a person's nutrient consumption can vary a lot from day to day and from season to season. For example, in more traditional, rural economies, fall and winter are typically when people eat more protein as that's when animals are slaughtered, spring is a pretty lean time when winter stores are depleted yet it's too early for new crops, and summer is all about fresh fruit, vegetables and berries.
If my chickens are any indication, they seem to self-correct their diets pretty well. If I supplement too extensively with fruit and veggie scraps, they stop eating them after a while, or only nibble at them before walking away, and that's my sign to hold off or go lower on produce for the time being. In the summer, when bugs, worms and grass are abundant, my chickens eat a lot less of their normal feed and barely care for supplemental produce as they prefer to forage.