I am also applying to MPH programs now with only an MCAT score (517) and no GRE. I already got into two of the programs I applied to (Temple and Mt Sinai).
You should first make sure that the schools you want to apply to accept MCAT in lieu of the GRE because there are a lot that don't. If they do accept MCAT scores then the GRE isn't entirely necessary, but a good score couldn't hurt your app. As long as you have a solid GPA and resume then you could definitely get in to some good MPH programs without taking the GRE.