From my view, it goes both ways: geometric algebra/calculus is a more transparent version of the standard approach and the translation back to it is also a relatively small delta to pick up.
Either way of going about what is in essence the same material entails becoming familiar with multivectors, the wedge product, and multilinear algebra, whether you do it through geometric algebra or the standard approach.
That makes sense but my argument is since further material (some examples which I listed) assumes and builds upon the standard approach, you'll likely be better off taking that path.
Either way of going about what is in essence the same material entails becoming familiar with multivectors, the wedge product, and multilinear algebra, whether you do it through geometric algebra or the standard approach.