I took this class in-person before reading ESL. I'd say there's more overlap between this class (18.650) and the class textbook All of Statistics (Wasserman) than ESL.

That said, ESL is a better companion than Wasserman if you want to apply the statistics to ML and don't plan on studying the graduate-level statistics courses. ESL + 18.650 + 9.520 (Statistical Learning Theory, Poggio and Sasha Raklin) covers 95% of the math and statistics I've seen in ML research.