If that was indeed the case. Then, it's broken in multiple way :
Hunter can just keep the first Abyssal Curse in their hand to progress their quest for free. So, while Warlock are already unfavored against hunter. If they are a Quest Hunter and you are a Curse Warlock, you should just concede turn 1.
I assume my opponent's Spell Damage (instead of my spell damage) will increase Abyssal Curse damage at the start of their turn. I doupt we will see the return of Quest mage with Arcanist Dawngrasp or the shaman trying anything with Bioluminescence beside some weird OTK.
Anyways... nothing I mentioned so far really mather because I had very weird result with Abyssal Curse deck. I either do 20+ damage in 1 turn or die without any chance of doing anything. But I did want to share the interaction between the hunter's Quest and the curse.
It's not really broken nor a faulty interaction, quest hunter doesn't suddenly become even more broken because some tier 4 deck has a bad interaction with it lol. Bombs from bomb warrior also trigger the quest. Also works with demon seed quest.