I looked up the plant... Appears to be very many varieties ,, and very pretty BTW.
Here are my thoughts views, and opinion.
Generally, chickens will not eat things that are harmful to them... They just know what is good for them, and what is not.
I have been keeping chickens for well over 20 years now. My chickens free-range in my back yard when I am there. When I'm not home, they have their secure run area.
There are a number of mildly poisonous plants around. My chickens do go among, and between them,,, but do not eat them. They choose to scratch for insects, and eat desirable greens like dandelions, and other grass weeds.
The toxic plants I am aware of are..
Daylilies
Yew tree
Deadly nightshade. (grows on fence from neighbors yard.)
I also container grow many different flowers,, including tomato plants. Tomato plants are in the Nightshade family. so are potatoes. The leaves are the part to be of concern. My chickens leave the tomatoes, and other flowers alone.
They do raid my container grown sorrel. I have to locate those containers out of their reach ,,, Or I would have no sorrel for myself.



So this is my view/opinion, why some chickens do ingest toxic plants.
If chickens are confined in a barren run,,, and the only green plant is a toxic one growing thru the enclosed fence,,, they may decide,,

, some green is better than no green.
I would not hesitate to plant your above mentioned plant inside your run, for shade.
WISHING YOU BEST,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
