regardless of whether it counts or not (contact some schools you are interested and see what they think), you will not learn in statistical physics what you'd learn in a statistics class.
In SP, you learn the statistical nature of thermodynamics. You derive some basic thermodynamic principles from probability theory.
In statistics, you learn very basic probability (nothing like SP), some probability distributions, regression, error analysis, and lots and lots of significance tests and hypothesis testing.
Other than use of probability principles, those classes are completely different.