Thanks for the responses.
Yeah, I've got a somewhat worthless B.A. in history&political science. It may serve me well if I opt for law school in ten years. For the moment, it just allows me to check the yes box next to the question that asks if I have a four-year degree. The enlistment bonus wasn't bad either.
But I was thinking of maybe earning a degree in electrical engineering or computer engineering or something like that. I want this and not something else like an engineering technology degree primarily because I already have a degree, and if I went to the trouble of earning another one, it would be because I'm seeking a specific career. When I search the ads on monster.com, it doesn't appear to me that engineering technology degrees are in high demand. They want engineering degrees.
Anyway, this would be roughly a 95-credit run for me rather than the usual 125 or so, since I've already got the non-technical/general education requirements taken care of. I was thinking of maybe asking for East Coast, which I imagined would land me in Norfolk, and I could perhaps take 6-9 credits/semester at ODU while serving.
From the responses, I'm hearing that this isn't very realistic. I know people who have done this, and that's why I was curious about the possibility. But none of them were nukes. And it seems the nukes who earned a degree on active duty went for an engineering technology degree -- or otherwise something besides a standard engineering degree -- through a variety of correspondence courses, distance learning, and other methods that aren't feasible for lab-heavy engineering classes.
So from what I understand, for whatever reason (ending up in the Persian Gulf on midterm day, the general lack of spare time, whatever), getting an engineering degree as a nuke on active duty isn't realistic unless you STAR reenlist, get picked up for prototype, and enroll at RPI.
This, of course, isn't what I was hoping to hear, but it's good to know all the same. I will adjust my plans and expectations accordingly. Thanks again to everyone for their responses.
If my reasoning outlined above is missing anything, feel free to add to it or correct it.