It is pretty easy to use it generate and test hypotheses, which is frequently done and published in the literature. Common examples include radio and other EM surveys for extraterrestrial signals.

By your definition, "Calculus" is highly unscientific.

Calculus owes some of its development to its use in scientific theories, but also stands alone as a branch of math. One can approach it as a pure exercise in symbol manipulation (as I did as a student).

Without trying to precisely define scientific methodology, I think it always needs some connection to empirical evidence. This is the problem with the Drake equation, but also with some other speculative fields like string theory.

So I'd say that the Drake equation is scientific in the sense that it's motivated by scientific speculation, but has not yet found a form that can be tested.