I'm 3 days away from finishing up grad school at a civilian institution while active in the Navy. The instruction that describes my program is OPNAVINST 1520.24B. Google it.
The deal w/ that program, aka "Scholarship Program," is that you have to find your own funding for at least 50% but no more than 100% of tuition+fees. If you're doing an engineering or science degree (the former in my case), usually most graduate degrees that require a thesis and research work have full funding. As an added bonus, most fully-funded research positions usually pay a stipend to support the student. Since the Navy's paying you already, you can't accept the stipend. That's actually a very good thing: you can use the fact that you're a "cheaper" student as a bargaining point, and your ENS pay is better than a grad student stipend.
Before submitting the app, I discussed the career implications of participating w/ the aviation advisor at my unit, and was told that I would have to kick butt whether or not I participated, so I went for it.
I commissioned through NROTC, did IFS (back when you could do it outside the Pensacola area), and started grad classes in the fall. Hurricane Ivan's effect on the pipeline in 04-05 also played a role in my decision. As for career implications, I've been commissioned for 27 months, and I haven't started flight school yet. I've been told I'll probably have a very short shore tour if I'm to get closer to my classmates and get back on track. Maybe I'm screwed.
Anyway, if you're considering this, I recommend you try to find a 1-year program. If you really want to fly, you might find yourself going a little crazy towards the end of a 2-year program. PM me w/ any more questions.