GRE scores come back pretty quickly; I think mine took about 2.5 weeks. After you submit sounds fine but I would look at the timeline for Georgetown. Most of the MD/PhD programs are pretty structured as far as when they are reviewing applications and when they offer interviews, so if you know your window you will be fine.
However, and someone can correct me if I'm wrong, though later MCAT scores will automatically go on your AMCAS app, I don't think you can put your GRE score in after you submit. But I am assuming this issue will be taken care of on secondaries anyway, yes? Plus, you will likely have your score sent directly from ETS to the school.