I would say that it is probably not solely responsible for making a man fall for a woman, but I'm sure it is a factor, especially if she is laughing at his jokes. That is one way to stroke a man's ego, especially if it is genuine. And if he is already falling for her, then her laughter can make her that much more attractive to him.
Men generally are attracted the beauty of a girl. But, there can be some odd scenarios where liking starts without even looking at a girl (online relationships). Different men have different needs. Some men prefer sex over everything. Some men prefer other qualities. Everything depends on the man in question here.
Making a guy laugh, by itself, won't win any man's heart. It might be small piece of the pie, but it takes a backseat to many other things such as looks, having an affectionate personality, finding him funny, and being low maintenance.