My memory says that Abe Lincoln also entered the presidency as an unbeliever. His final writings suggest he came to believe. The job humbled him. The same with Nebuchadnezzar.
Frankly, I would prefer an unbeliever to someone who claims to be a "Great Christian" and has never once repented of his sins (that would include the deadly sin of pride).
I think I would have to number an unrepentant sinner who calls himself a great Christian amongst the unbelievers.
Am I wrong?
Is not repentance the very foundation of forgiveness and salvation?