I believe the program is known as the Immediate Graduate Education Program (IGEP). It comes in several flavors. Certain ones will send you to military graduate schools to complete your degree in a year, other versions will allow you to remain at a civilian school for up to two years.
I was selected for the program and went to the Air Force Institute of Technology for a one year Aero Engineering grad program. I have friends who have done the civilian school program. I know the civilian school program requires you to find funding to help pay tuition and fees, but it sounds like you have that taken care of already.
As far as timing goes, well there are two schools of thought. The first, think its a bad idea because it puts you behind your year group and you have to play catch up. I can understand this with a 2 year grad program, but with a one year grad program it won't make that much of a difference. I, personally, am only about 6 to 8 months behind the people I graduated from school with. So, I can still easily catch up to my peers and I have a grad degree already...good deal in my book.
The second school of thought, and the most common one, be glad you got your grad degree early. If you stay in the Navy for a career its kinda expected you get a grad degree to advance past 0-4. Second, an engineering degree will open a LOT of doors to you down the road (TPS, AEDO, AMDO, and other engineering related fields).
Personally, for a one year grad program, get your Masters degree and get it done. You'll catch up to your peers quickly. School may suck while you are there, but you'll be glad you got it out of the way early. I haven't seen any benefit to having my Masters in flight school, but I know I will be glad I have it a couple years down the road when I make decisions concerning TPS or AEDO. That or when I get out of the Navy and look for a civilian job.
Hope that helps.