Yes, but there must be some logic to one's belief. But logic is not a proof of any truth since it is independent of the content of its subject matter. Logic is only a reasoning method. Therefore, to believe or not to believe in an Avatari is a choice. His purpose is to teach the believing soul with gentle persuasion that it choose the path of the conscience.
Humans nurture pride and greed for pomp and power.
Therefore more so the need for the Avatari to be present on earth to demonstrate the exemplary life. The human form of the Avatari acts and does all things human within the human constraints so that neither he nor his near ones are deities. History is the final judge. The lives of Abraham, Buddha, Confucius, Socrates, Moses, Jesus, Mohammad, and all such great spiritual beings who lived on this earth are proof that lives can be lived exemplarily and fearlessly. The Avatari presents a fresh interpretation of the revealed word in an everchanging world.