I found this article where someone has actually done an experiment https://cleantechnica.com/2018/04/16/how-ev-range-is-affected-by-quick-acceleration/
Conclusion: "The state of charge on the first day on my return was 33%, and the state of charge on this next day on my return was 40%, making a difference of 7% in the state of charge over a 30-mile journey."
so yes, accelerating fast does use more energy overall.