Whenever I've whisked yogurt, I've noticed it breaks down and turns liquidy. Regular yogurt especially will do this, so I'd worry that the icing will be too runny and not set. I wonder if Greek yogurt might do the same.
If you are concerned about calories, the cake is yummy without the frosting. Serve it dusted with powdered sugar or with a fruit sauce, like puréed raspberries.
Here's a fairly recent thread on the cake. Yogurt will be very tangy and possibly too tangy, but that's all up to personal taste. I think you'll find some comments on using yogurt in the recipe comments as well.
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If you are concerned about calories, the cake is yummy without the frosting. Serve it dusted with powdered sugar or with a fruit sauce, like puréed raspberries.
https://food52.com/hotline/33056-a-question-about-a-recipe-chocolate-dump-it-cake