Average army morale and global popularity

Global Popularity does not affect damage at all. Armies also don't have morale, they have hitpoints (or health). So morale also doesn't affect damage output. If by morale you mean hitpoints/health, then this indeed affects damage output. An army super close to 0% health only deals out 20% of its usual damage. Between that and full health a linear curve is used.

Please read the popularity in depth guide here: Popularity with Elite AI