I am not a doctor, but I would say emphatically, no it is not safe while breastfeeding.  Your body would not get enough calories...you're already in need of 500 more calories per day just to produce the milk.  If you can pump extra for a week, then have the milk on-hand to feed from a bottle while you diet (and then pump and dump what you produce while on CSD), maybe you could do it.  But please give your body the calories it needs while you're breastfeeding.  Plus remember that whatever you eat, the baby eats, and the CSD tends to be loaded with many gassy foods.

Remember I'm not claiming to be a doctor or expert, but that's my two cents...

Not only are you not getting enough calories for your baby, most babies can't stomach cabbage, it's makes them colicky. That's all you need on a tough week of CSD!
No, I would not do it whilst breastfeeding!