Yes. (I read the flashback and saw.)
But here are some crumbs for thought.
1. We don’t know when Oden started using CoC passively to tame Enma, but we know he was using it when he met Whitebeard even though he himself didn’t know it.
2. The sword was a birth gift. Kozaburo wouldn’t give a deadly sword to a child, therefore like we learn this chapter, it’s likely the sword automatically accepted Oden as it’s master. Swords have done this before (Sandai etc.)
I should note that a sword accepting an owner doesn’t mean the sword is mastered, but rather sword can be wielded without threat of death to the owner.
3. Oden had no problem giving Enma, a deadly blade, to his daughter. Meaning the sword can likely just accept an owner, like I said above(like Shusui wanting Zoro). And as Kozaburo states, swords have their own personalities.