Hi there,
Crazy to see someone in such a similar position! I've also been admitted into the CMES program at Harvard, but didn't realize that they would not be amenable to deferring in favor of Fulbright (something I was hoping to do). Who have you spoken to, and what have they said exactly? This worries me tremendously :-(
As to your question: I've been in DC for a while now, and the Georgetown Arab Studies produces excellent graduates that are primed for government service. If you have the opportunity to do the Fulbright and come back to Georgetown, you'd also have time to apply for fellowships like the Pickering, funding your M.A. degree and basically promising you a career at State. My two cents!