It wasn't a timed quest, and I can confirm the quest didn't disappear when I did this. If it did on you're account that's an odd glitch, you could fix it by creating a new character and doing the quest on them. Would mean resetting your quest progress if you're already using all 3 character slots though.
I am already using all 3 chars so I'd rather not do everything over again. Are all the quest steps called Cayde's will?