Yes, in some cases. Pets will definitey show sadness when a companion dies. I've seen both bird and squirrels run back to an injured mate and try to help it. When the mate died, the other one seemed quite distressed.
Wild animals, unlike humans or domestic pets, move on very quickly and don't seem to care unless the dead one is a mate or a sibling. As an example, the members of a herd are not going to care if one goes down by a predator. The are too busy responding to the instinct of danger.