Define "work." If the only goal were losing water weight, it probably does work. If the goal is a healthy way to lose weight, it probably doesn't, because your body does need some other things the Atkins religion doesn't provide.

So saith the dietitian I have known, who is extremely frustrated with fad diets that omit segments of a healthy diet and contribute to her ongoing war with eating disordered clientele.

I have also known someone on a somewhat modified Atkins diet... he had the worst BO ever.