The question defeats itself by a false premise. It devises a question about faith (that leads to works) and then questions can a person with such faith not produce works and yet by very definition such a faith WILL produce works. The question is circular, and leads to a forced premise that is backed by false premises.
This being the case, the answer is neither "No", or "Yes." It needs to be re-worded. As is, the question is a false dichotomy. It puts up two answers and yet requires another. The question (and point) defeats itself.
Salvation MAY lead to works, but such works do not merit salvation as it is already theirs. If works do not flow from such salvation, we do not assume they are not saved. Works are a witness of being saved, works are for you and others. However bad a witness someone might have, we do not condemn them. Look to the Corinthians who slept with temple prostitutes. How quick some in the body of Christ would say they are not believers. Yet Paul calls them saints.
I say, "Salvation MAY lead to works" because there are factors to consider why a person may not reap such works. Consider death bed confessions. What work can they do upon being a moment from death? What of a stranded man, who comes to revelation of Jesus and has no one to do good to? Lost on an island and yet Jesus visits him. Is such a man condemned because he could do no good to man? Do you not see the self-righteousness implied in this question?
Let us not forget that men will be saved "yet so as by fire." They will have no works remaining and yet they are saved. So can a man have faith and yet produce no works? Yes, and a resounding yes. We could give example after example, and hypothetical scenarios left and right. It is not to a person's advantage to not be able to produce such works, however. It is bittersweet. They are saved, and yet no rewards. If salvation was dependent upon the works we did, we would be better off isolated on an island, or being a deathbed confession, in order to secure our eternal destination. How sad would it be that God desires us to love others, and yet sets in motion a plan of redemption that sets us apart from doing so? "Love others at your own risk", would be our motto.