My party played Hoard of the Dragon Queen without a Cleric or a Paladin and did very well. Our party consisted of a Druid, a Rogue, a Warlock, a Sorcerer and a Barbarian. The Druid was the main healer but the Barbarian always had healing potions with her.
When we started and our Cleric was leaving just prior to Hoard of the Dragon Queen I put up a question about healing optionoptions with a cleric. The Inspiring Leader feat is quite useful. Healing options for non magic users. The Barbarian also had a Healing Kit but I don't she used it more than once or twice.
We actually went on to play Rise of Tiamat and with a party of five level sixteen heros managed to kill her with only one member of the party dying, and we had a potion to bring him back to life.