Yes it's behind everything a derivatives quant would do. But I think quite a long way behind. Closed form analytic solutions using calculus only exist for relatively simple models and products. Most of the time you use it to calibrate and discretise a model and afterwards it's all Monte Carlo. What's more you can often just look that part up as models are increasingly commoditised rather than secret sauce.

Stochastic calculus is required to derive closed formulas and approximations used to calibrate SDE models. Similarly to deep learning, the secret sauce lies in the training, less in the inference. The code used by banks is closed source, and the research papers are missing said secret sauce. Calibrating models in a production environment handling correlation, multi-curves, stochastic funding, discrete dividends, etc. is not a solved problem. Interest rate derivatives modeling heavily relies on change of measure, even when using simple models.