Can someone be godless?
 
Doesteyevsky thinks not.  Here's his thoughts from The Adolescent (pp. 372-73):
 

"Perhaps even now, though," Makar went on with concentration, "I'd be frightened to meet a truly godless man, but let me tell you, Doctor, my friend, I've never really met a man like that. What I have met were restless men, for that's what they hsould really be called. There are all sorts of people like that and you can't tell what makes them the way they are: some are important, others are little men; some are ignorant, other are learned; and they come from all classes, even the lowest... but it's all restlessness.  For they keep on reading all their lives and, having filled themselves with bookish wisdom, they talk and talk, although they never find answers to what's bothering them and remain in darkness.... A poor man may be short of bread, may not have enough to keep his children alive, may sleep on rough straw, may be brutal and sinful, but still his heart may be gay and merry; while a rich man may eat and drink too much and sit on a pile of gold with nothing but gloom in his heart. A man may study all the sciences and never get rid of emptiness and gloom; indeed, I think that the more intelligence he gains, the more his gloom will thicken. 

"Or let's look at it this way: people have been taught and taught ever since the creation of the world, but what have they learned in all that time to help make the world a gayer and happier place where man can find all the joys he's longing for? What they lack, I tell you, is beauty.  Indeed, they don't even want it.  They're all lost and every one of them glories in what has brought him to his ruin. But they never think to face the only truth, although life without God is nothing but torture. What it all comes down to is that, without realizing it, they curse the only source that can brighten our life. But that won't get them anywhere beacause a man cannot live without worshipping something; without worshipping he cannot bear the burden himself. And that goes for every man. So that if a man rejects God, he will have to worship an idol that may be made of wood, gold, or ideas. So those who think they don't need God are really just idol worshipers, and that's what we should call them.  But there must be true atheists too; only they're much more dangerous because they come to us with the name of God on their lips...."