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 Rouge, 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 option with a cleric. The Inspiring Leader feat is quite useful.