I'm gonna echo everyone else here: It depends on the difficulty of the quest, and the skill of the player. The First Quest of Z1 is pretty easy, I could easily see getting through it without potions or fairy ponds (I wouldn't do it, but I'm not very good and I like having full life as much as possible), but trying to do something like Armageddon Quest without either is probably not recommended.
(Emphasis, mine.)
Strike that, and ponder if it is possible.
TeamUDF certainly has many LPs where he doesn't use potions.
Drop rates for hearts, faeries, and such is also critical, alongside general skill, input issues (controller directionals, or other latency), and other factors other than sheer quest difficulty.