Nope, Zack and Cloud both survived. Head back to the Shinra Mansion in disc three, and go to the basement - you'll get shown a cut-scene where Cloud finally regains all his lost memories, and has a flashback to the time when he and Zack escaped from Shinra.
Cloud really did look up to Zack as a 'role model', the kind of guy he wanted to be; but he only adopted that make-believe role because he wasn't able to resist Jenova's mind-altering effects.