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.
Curious. What does 'background' mean in this sentence. You can spend years studying just one of these in depth. How much is "enough" for ML?