So if we are going to get crazy pedantic with it, technically no. Actors (players, minions, enemies) don't have added damage effectiveness. Each individual damage source has an added damage effectiveness. Most ability objects have just 1 but some can have multiple and each ability can create multiple ability objects (e.g. volcanic orb creates several different types of ability objects depending on how it is specialized).
If a minion or player use the same ability, they get the same added damage effectiveness. Because minions get way way way less added damage in general, their abilities have much higher base damage so they can still scale effectively with % damage stats in the late game. This means that because they have different abilities, those abilities have their own added damage effectiveness stats so minions kinda in a roundabout way have their own added damage effectiveness.