I think this would apply to grass allowed to form seed heads. Then, the combined analysis of all parts probably would contain a higher amount if protein.
No it would not be bad. Protein is not the evil demon that people once thought it was. Most species are opportunistic scavengers in the wild and will even eat meat if they happen upon it. The way to stop it from going to seed is to keep it trimmed. You can do this with your tortoises, a weed wacker, brush buster or lawn mower.