It seems to me that everyone leads a complete life -- utterly complete. No one walking to the kitchen believes s/he is walking to the kitchen. S/he is completely walking to the kitchen. No one riven by grief believes she is sad. S/he is completely sad. Everyone leads a complete life ... and then brings belief to bear.
Belief relies on two things -- doubt and the past. To believe something is to place it at a separated distance based on a past that cannot be grasped. But is there anything graspable or ungraspable about walking to the kitchen? I don't think so. Walking to the kitchen is complete -- a whole life in ineffable action.
If any of this is true, then I think belief might be described as an incomplete expression of a complete existence. Belief may be integral to a complete existence, but it can never complete it.