They absolutely need each other in their attempt for leadership. Piggy needs Ralph's charisma and natural leadership, and Ralph needs Piggy's rationale and intelligence. However, Ralph also recognized the downfalls of Piggy(physical appearance, un-usable ideas) and didn't always trust what Piggy had to say.
One of my students last year paralleled President Bush and VP Cheney to Ralph and Piggy. At the risk of starting a political argument, that's probably not a bad example...
Ralph is the leader. Think of him as something like the chief of the tribe that is forming on the island.
Piggy is the equivalent of the tribal priest or medicine man. He is the thinker. He isn't Ralph's match in charm or physical prowess, but he can come up with key ideas and symbols (like the conch). Ralph needs him for his brain and spirit, just as Piggy needs Ralph for his body, his charisma, and his ability to act.
the relationship is a symbiotic relationship were both need each other to survive. Ralph needs piggy for ideas and piggy needs Ralph for self preservation needs.