How often do you exercise when on a water fast? Not so much weights as there is no protein to repair but other exercise?
If you have a lot of excess bodyfat, like more than 50 pounds or so, you can do weight training while fasting. Your own bodyfat breakdown will supply any amino acid need to repair damaged tissues.
If you are lean, then no, but most people do fasting because they are trying to lose a few pounds right.