Hah! Yes, the chickens provide plenty of entertainment by themselves, but with mulberries added to their repertoire it'll heighten it! :>)
I had a small orchard area, 23 dwarf fruit trees, and allowed the chickens access to it. They'd eat the fallen fruit, bugs, etc, and everyone was happy. I bet your mulberry will be the star of the show in your chicken pen, or at least the MC!
Hope all is well your way.
Stay warm. Stay dry!