I only eat no fat Fage yogurt. What happens if I use it in the recipe?

The less fat you have, the more prone the yogurt will be to separating and not staying creamy when it encounters heat or something acidic—hopefully that won't happen with this recipe, but I'm not sure. Nonfat yogurt also won't round out the bitter chocolate flavors as nicely. It still could be worth a try, and I would just aim for a type of chocolate that tastes a little creamier and rounder on its own, maybe more in the 50-60% cacao range than 70+%.