If you've never taken a course in data structures and algorithms - take one. Especially if you'll be tested on them; it seems like the obvious thing to do.
Would going through the entire course, along with coursework and readings provide enough understanding to forego Leetcode and to start interviewing?
Probably not. You need to practice. As a fellow self-taught engineer, I'd say it's worth doing. Check out something like algoexpert.io or one of Andre Neagoie's courses on Udemy to get a mix of theory and practice.
Take the class and do some leetcode practice. Also, don't look for shortcuts.