You are correct that nothing will happen. The Champion's abilities are what are called Linked Abilities, and the second one depends on choices made from the first one. Since nothing was targeted by the first ability there is nothing for the second one to reference.
Think of it like Fiend Hunter since the first ability didn't exile anything there is nothing for it to return when it leaves the battlefield, the Champion works the same way but with life.
607.1. An object may have two abilities printed on it such that one of them causes actions to be taken or objects or players to be affected and the other one directly refers to those actions, objects, or players. If so, these two abilities are linked: the second refers only to actions that were taken or objects or players that were affected by the first, and not by any other ability.