Yes. All units heal automatically. Each type of unit has a Morale that will directly impact the development of that troop, I mean the power of Attack and Defense. An example of this is the Bomber Plane that if it stays in combat for a long time its Morale gradually decreases. But if after a fight you leave the Bomber Plane resting, its Morale will gradually increase. This goes for all units. "Don't confuse the Morale of units with Hit Points."