I think you will find that is a big no as the toxins in your body can be released through your breats milk.
Are you saying the shakes are full of toxins or losing weight causes toxins to be released?

Every time I've breastfed I've lost insane amounts of weight, the first time far too fast. I bought the non-diet versions of those shakes as a supplement. The ones in the 'gain weight' section of the health aisle. They didn't do much, so I quit BF.