You can definitely use eggshells in your succulent garden! Instead of crumbling them up, I would suggest making a tea out of them.
Rinse the shells so they're free of any yolk or white, and then pour boiling water over them. Allow them to soak over night, and then strain the shells out the next morning. Pour the “eggshell tea” on your succulents to give them an added calcium boost. This may also give them some extra potassium, but is lacking in nitrogen, an element that succulents need, so you may need an additional fertilizer that contains that.
My favorite fertilizer to use is Haven Brand's Manure Tea. If you choose something different, like a cactus fertilizer, be sure not to purchase a slow release fertilizer, as it can burn your succulents.