Theoretically it's supposed to work. With the decrease in energy from carbs in your blood stream you'll experience a large amount of die off originally. I don't think it's ever possible to fully rid it with diet however as your system won't fully be able to tell whether it needs the gluconeogenesis for it's own cells or for the yeast cells. Your best bet for fully ridding yourself of the infection is to go on both the diet and get the systemic pills. The dangers of something like nystatin or diflucan aren't really severe and you don't have to stay on them long either. They are however proven to be severely effective.
Personally the diet only greatly diminished the infection, had to take an antifungal to get fully rid of it.