It’s not the hot manure that kills things off so quickly, they peck and eat the green stuff. And they scratch a lot. They especially like to eat things that are just sprouting.
I can’t tell you what will happen at 20 square feet per bird. That’s going to depend on how well the turf is established, how old the chickens are (young chicks don’t do as much damage as adults), your time of the year, and weather (heat and rain). In wet warm weather grass can grow pretty fast, in a dry spell or over winter if gets wiped out pretty fast.
One of two things will happen. They will strip it bare so nothing grows or they’ll keep the stuff they eat pretty well eaten down but the stuff they don’t like will grow and take over. I have to mow mine three or four times a year to knock down the bad stuff so the stuff they eat can grow.
What is your native grass that they will eat, Bermuda? That’s what grows here but you are probably drier than I am. If you can get a turf established of a grass that grows well in your area and keep it watered this summer when it dries out you might keep it growing this summer, but at 20 sq ft per bird I think that will be a pretty big challenge. Thinking on mine, I don’t hold out much hope for you, but you might surprise me. The only way to find out for sure is to try.
A couple of thoughts. If you can have two different pastures you can let the grass and other stuff recover on one while you graze the other. Alternate from one to the other. Another thing that people do is make a grazing frame. Make a frame on the ground, maybe with 2x6’s, and cover it with wire mesh, say chicken wire. When the grass and other stuff grows up through that they can eat it off without taking the roots out.