Pope Francis suggests that it is possible.
But the pope, in a morning Mass on Wednesday, suggested that belief and faith weren’t the biggest factors. He said, CNN reported: "The Lord has redeemed all of us, all of us, with the Blood of Christ — all of us, not just Catholics. Everyone. 'Father, the atheists?' Even the atheists. Everyone. We must meet one another doing good. 'But I don’t believe, Father, I am an atheist.' But do good: We will meet one another there."
This is sure to spark a wildfire of outrage. The idea that good works can earn salvation really pisses off some Christians. Grace is presented as necessary and sufficient for salvation. In less extreme sects that grace comes as the result of a choice the individual makes to be saved. In its more extreme forms -- Calvinism for example -- the saved were selected at the creation of the world and how each lives his life doesn't matter. At neither extreme, nor in the middle can grace be earned by action. It is a gift from the Christian God and character or conduct have nothing whatsoever to do with the salvation of the soul.