To start, why do you want to be an officer? Do you know what they actually do? Next, why specifically nuke?
Now, for your questions. For viability, both are viable options, but neither is guaranteed. If you want to be an officer, don't enlist, get the degree and go that route. I believe there are more options than just NUPOC for the college route (e.g. Naval Academy, NROTC). As far as paying, I expect you pay for out of state tuition the same way as in-state, scholarships, loans, jobs, etc. At some point, NUPOC would start paying.