Correct. So the faith present in the works saves him despite the declarative faith being to the contrary, whereas declarative faith not present in the works does nothing. Compare:
A certain man had two sons; and coming to the first, he said: Son, go work today in my vineyard. And he answering, said: I will not. But afterwards, being moved with repentance, he went. And coming to the other, he said in like manner. And he answering, said: I go, Sir; and he went not. Which of the two did the father' s will? They say to him: The first. Jesus saith to them: Amen I say to you, that the publicans and the harlots shall go into the kingdom of God before you. (Matthew 21:28-31)
Lord, when did we see thee hungry, and fed thee; thirsty, and gave thee drink? And when did we see thee a stranger, and took thee in? or naked, and covered thee? Or when did we see thee sick or in prison, and came to thee? And the king answering, shall say to them: Amen I say to you, as long as you did it to one of these my least brethren, you did it to me. (Matthew 25:37-40)
I don't know why you can't see that you are STILL saying works save apart from faith. There will no doubt be many well meaning, "good" atheists in hell. At least those in heaven who did good to the Lord through their kindness to the least of His brethren believed that He was the Lord.