[hershkumar]

Practically speaking, QM can be taught without the assumption that students understand the Hamiltonian formalism, simply by starting with Hilbert spaces and operators on Hilbert spaces. In fact, I would claim that having taken a class on basic linear algebra would better prepare you to understand quantum mechanics than mastering classical mechanics. QM is generally taught by referencing classical mechanics, but I believe that's more reflective of the fact that most universities require classical mechanics as a core course, and students coming in to QM will have generally taken it.