> How are general-relativistic effects relevant for the outcome of the Michelson-Morley experiment?

General-relativistic effects are relevant for the outcome of the Michelson-Morley experiment in the sense that the general theory of relativity is a generalization of the special theory of relativity. :-)

Otherwise: the additional predictions that the general theory of relativity makes about gravity, curvature of space etc. are not relevant for the outcome of the Michelson-Morley experiment.