I believe that you can use Feynman diagram machinery can be utilized for ANY purturbation theory as long as you can justify the smallness of(where coupling constants involvedare smaller than unity, e.g. QED) as well as non-perturbative theories (which is the case for QED theory but not for QCD theory wherewhere coupling constant is on the order ofconstants are larger than unity, e.g. QCD at low energies or large scales). This is pointed out by Bjorken and Drell,
The Feynman graphs and rules of calculation summarize quantum field theory in a form in close contact with the experimental numbers one wants to understand. Although the statement of the theory in terms of graphs may imply perturbation theory, use of graphical methods in the many-body problem shows that this formalism is flexible enough to deal with phenomena of nonperturbative characters … Some modification of the Feynman rules of calculation may well outlive the elaborate mathematical structure of local canonical quantum field theory …
However, let's remind ourselves too that these diagrams (taken individually) are only a representative of the reality rather thanin the sense that they represent the trajectories of particles in intermediate stages of any scattering process. This literally means that it is their summation that would represent the reality itself. But they are good representative meaning they are simplifying our calculations drastically especially when equipped with high level programming.