If we falsified quantum mechanics we might expect some formalisms (Hamiltonian, Lagrangian, path integral, whatever) to continue to work while others don't. So

If we falsified quantum mechanics we might expect some formalisms (Hamiltonian, Lagrangian, path integral, whatever) to continue to work while others don't. So it's perfectly possible to falsify the idea that path integrals do not describe the world; doing so would demonstrate a failure of quantum mechanics and would be extremely exciting to physicists.