Yes, the electroschematics website describes an led load being powered by a capacitive drop supply.
I'm not sure which we would say: whether the led load complicates things, or whether it simplifies things.
It's all right to use the simpler formula with the led, because it creates its own voltage drop, and thus it automatically causes a greater drop across the capacitor than there would be with a plain resistive load.
LED's are non-linear components.
I used the idea of a resistive load because it is linear. It is a simpler case with which to illustrate the concept of voltage drop.