Do you think advanced classical mechanics is useful for quantum mechanics?
It depends on what your ultimate goal is. If you are serious about physics, then the classical mechanics is critical for your understanding of the entire field. I think about classical systems all the time when I am thinking about quantum systems. You can’t really know how they are similar and how they differ, if you only know one side. I would absolutely say that the intuition gained while doing advanced classical mechanics will benefit you in quantum. Many of the techniques are similar, or at least analogous in some way. But, if you aren’t going to go into physics, then you do not need a broad background.