Might they even do more the stack but work of each other.
Heroic Echo (Su): At 3rd level, when you receive a morale bonus from any spell, spell-like ability, or magic item, including those you cast on yourself, that bonus increases by +1. At 9th level, this ability also applies to competence bonuses. If you receive a morale effect (or a competence effect at 9th level) that affects an area or multiple targets, as an immediate action you can share your increased bonus with all other recipients. This increase to other participants lasts a number of rounds equal to your Charisma bonus. You can use this ability once per day, plus one time per three levels after 3rd.
Courageous
In addition, any morale bonus the wielder gains from any other source is increased by half the weapon's enhancement bonus (minimum 1).
It is too bad that a barbarians rage is not a spell, spell like ability or or magic item or it might be worth to multi-class.
RAW, yes. They both add untyped bonuses to another effect.