I wouldn't recommend the diet, but I do recommend adding an apple cider vinegar to a sensible diet to help lose weight. An added bonus, and this sounds crazy but it is true, is that apple cider vinegar supplements help with heartburn/GERD symptoms.
You will lose weight, but after you get to your goal weight and eat normal, you will just gain it back. I advise that you should go on a healthier diet with balanced meals and a exercise routine. You will lose weight with that.