In one sense, the atheist might believe in natural moral law; in another sense, he already believes in it; in yet a third sense, he cannot believe in it.
He might believe in it in the sense that nothing prevents him from responding “Yes, that’s true” when presented with the proposition “There is a natural moral law.”
He already believes in it in the sense that he possesses the "natural habit" of the knowledge of the first principles of practical reason. It isn’t because of our theories that we know the moral basics; they come with being human. Our theories come afterward and try to explain them.
But he cannot believe in it in the sense of holding premises consistent with it. True law presupposes a lawgiver superior to the one to whom the law is given, and the atheist denies that there is such a being. If he supposes that morality is something else, such as instinct, he misunderstands what law is.