If by "healer" you mean a mage specifically meant to heal others and cast buffs on party members, then yes, I did it at least 4 times. (out of the 7 times I played through, 5 of which were the notably more difficult PC version) But then, I knew where all the best stuff was, where the ambushes were, which areas were best avoided until later on, and which choices resulted in X and Y attacking or settling their differences without murder. Not something you want to try on your first go, I think.
If you mean without anyone healing by any means at all, (potions, blood magic, certain abilities, POTIONS) why would you want to try? Not sure it's impossible, but the Arch-Demon would be a real ***** no matter the difficulty setting, I think. Seems like one of those "Go through the entire game with no weapons/armor, one party member, and an enraged chimpanzee assualting you with a frying pan" type quests taken up mainly by lunatics.