Light gathering in M43 vs FF

Light and luminosity aren't the same thing. At least in what is probably your understanding of luminosity. But since you bring ISO into the equation, it should be said that ISO sets by its very definition the ratio between 'brightness' at the sensor and 'brightness' in the final image. Thus when asking whether the same exposure yields the same image brightness when keeping the ISO constant, the answer is yes, by definition (of ISO).

(And that is a simplified answer as there are several slightly different definitions of ISO.)