Faith can, and should lead one to good works. I don't find that good works lead to faith. I first thought of this in terms of social action, noting that those who become involved in good works are in danger of redefining their faith in terms of the work. This audience will think first of liberals being in that danger, but there are those who take on education, especially homeschooling, as a task, or work for a candidate or political cause and come to see that as their mission.
They may earn respect from their secular colleagues, which feels like good PR for the church, but I don't see that they ever pass any of them back to us. It just doesn't work that way somehow. Dietrich Bonhoeffer thought that it might, and encouraged Christians to work on secular causes they believe in for that reason. Good works should be done whether they attract people to Christ or not. Yet I think people will be less tempted to be consumed by them if they lose the illusion that very many will come because of the works.
It may be that good works sustain faith in those that already have it.