I certainly think so.
If an important, old, or good number of hen(s) disappear, the remaining flock's production will drop.
If a rooster goes that a hen really liked, she gets a little down. I once had a pair free ranging, and the rooster went sick, nearly on his death-bed. Before separating him, the hen would literally try and lift his body up, and when she couldn't, she'd stand there by his side until I moved him to quarantine. It was sad but sweet.
My last encounter with loss affecting other birds was the loss of my Shamo hen, which had my normally very dominant, bird-aggressive, and proud Shamo rooster suddenly go submissive, shy, and crow-less for weeks. (by submissive I mean any encounter across the fence with another rooster resulted in a turn-and-flee reaction)
Chickens are some vicious, very hierarchical animals but also some very communal, emotional ones too.