If I am a Celestial Warlock and I take the Magic Initiate - Cleric (Cure Wounds), does that now count as a Warlock spell for me? [duplicate]

Question

If I am a Celestial Warlock and I take the Magic Initiate - Cleric (Cure Wounds), does that now count as a Warlock spell for me?

Since under The Celestial it says: "The following spells are added to the warlock spell list for you." and Cure Wounds is on the list.

This last part in the SAC would lead me to believe yes: "In short, you must follow your character’s normal spellcasting rules, which determine whether you can expend spell slots on the 1st-level spell you learn from Magic Initiate."

Bonus question, option 2: If i took the feat after having one level in Celestial Warlock, could I take Cure Wounds using Magic Initiate - Warlock.

Answer 1

According to this answer, a spell is considered a Class Spell if it's listed in the class' spell list. So given that the Celestial patron adds it to the Warlock Spell List I would say that it does count as a warlock spell and can be cast as such.

Worth noting though is that after testing this with the DDB Character Sheet it doesn't seem to be treated as such. You get the single use from the feat and that's it.

As a DM however I would rule that it does count as a Warlock spell and can be cast using a pact slot as if you had learned it normally.