I would say "No". And it's my field of study. I think, if you include probability, then there's a good case to be made for "Yes" as well, but I'd say that statistics is more about applying math properly. If math includes its own application:
There would be no such thing as statistics if not for mathematics.
Nor would there be many, many things. Math is a wondrous "subject", if it's appropriate to even call something so fundamental a subject. By your definition, everything is math. And that's an appropriate answer. This is only a matter of semantics, anyway.
College-level Statistics is a total BS subject. I had to endure a whole semester of it and only barely passed by the slimmest margin.
Well, it's just one semester. You seem to have a sample size issue there.