Yes, chickens will eat mice. They are very partial to all insects and I remember my uncle decided to keep chickens and bought them before he had build a coop so put them in his finch aviary. The next day there were only two scared finches left, the other half dozen or so had been gobbled up by the chickens.
They will go for protein whenever they can. Pheasants, turkey, peafowls etc. are all the same, no mouse/vole or insect is safe around them.