Only if they were to walk on it constantly. Most will decided it's uncomfortable on their feet and stay off it. I like to do several small "plots" so they can access it from all sides without walking on it.I'm curious about the wire topped boxes - walking on them doesn't hurt their feet or cause bumblefoot after a period of time?
As far as other plantings go, here is a list of chicken safe plants. It even lists the zones for most of them.https://www.backyardchickens.com/a/safe-plants