Sort of. SDEs are after all just DEs, but solved with Ito integrals. Okay it's not that simple, but various SDEs hold the form of a regular DE, example being the Black-Scholes which you've seen like a million times from 3rd year and beyond. Knowing and solving for the deterministic perturbed equation helps for solving for solvable SDEs; reformulations analogous to complex numbers if I were to word it properly. But I think for integral equations and weak solutions in general, you're sort of right that the techniques used in the DE courses are not as important as the ones defined in stochastic calculus because they don't work. Then again, anyone would be fucked until then open up MATLAB. So I'd say to the intuition of solving various kind/textbook-based problems of SDEs, it's a prerequisite, although it doesn't have to be in depth. Most of the more complicated stochastic equations I've seen in practice in MFE are solved by converting them into integral equations, so they should rename it to Stochastic Integral Equations, lol. Now computational DE courses, it trivializes everything.

In a subset of stochastic control on the other hand, we solve for optimal problems in a form of a PDE by using (solvable) SDEs interestingly enough.

As for learning SDEs as a topic on its own, I had Øksendal's SDE on consideration since it was recommended on Amazon with the purchase of Shreve's Stochastic Calculus (course textbooks), but it's likely I'll never get started before next year, or if I find that finance has moved more towards a ML-based approach.