I'd say slightly more. Maybe it's just because I attended a state school, but I think my first semester calculus class was all single variable (20 years ago now, so my memory is rusty). You really to understand gradients and jacobians for ML, which I think was calc III for me. But you can skip curl and div part I guess.
Not much of your calculus book will be relevant beyond the first couple of chapters, but you'll live and die by the numerical-method sword. The idea is that you need the analytic insight from the former to understand the latter.