Orphan is most definitely a Fal'Cie. His purpose is to power Eden (but I'm not sure about the other Fal'Cie). Eden is the nexus between all the other Fal'Cie, making them interact with each other in a way that Cocoon worked. By killing Orphan, the Fal'Cie stopped operating in this manner, and Cocoon came crashing down in spectacular fashion.

The whole Fal'Cie thing on Cocoon reminded me of the Death Gate Cycle series of books. But the clear thing is that Orphan is a Fal'Cie created with the sole purpose of acting like a battery.