I don't know about Deep Learning Nanodegree, but I took Machine Learning and AI Nanodegrees at Udacity and they are definitely worth it. I would not recommend them to total beginners in the field. You need to have at least some experience with data science and Python to be able to follow along. Do some free courses on Udacity, Coursera, EdX and other platforms, try to implement these algorithms with your own data and problems and then take the Nanodegree to fill the gaps.