what jobs are available to an individual once they receive the TESC BSAST. What jobs would they be considered for being hired based on having this degree?
In the strictest definition, your son is not going to be a "Navy Nuclear Engineer" as an enlisted nuke without an engineering degree. He's going to be a "Navy Nuclear Operator". So, how one bridges the gap between NNPP Operations and civilian engineering (nuclear or non-nuclear) is a complicated topic, but yes a college degree will be required. The transition between Navy Operations and Commercial Nuclear Operations does not require a technical degree, as posted already.
The academic path to the broadest range of technical opportunities, assuming your son has no clue what he wants to do after the Navy, is a full engineering degree. If he wants to do nuclear research at a DOE lab, than a PhD or DE is required. If you look at the various job postings floating around the Internet, you can see what employers are looking for in their technical candidates in 2009. Some "need" a full engineering degree AND a Professional Engineer's (PE) License. Others want "just" a technical degree (TESC, Excelsior, etc). Also, he doesn't need a BSNE to work in nuclear...BSME, BSEE, etc. are also needed at nuclear sites, particularly in post-Navy federal employment, which seems to have the strictest academic requirements of any employer.
If your son wants to transition from the Navy into Commercial Operations, then as posted already...a degree is not required by the NRC, but many other prerequisites have to be met. However, any Utility can ask for "more" than what the NRC deems the minimum to be. I believe that if your son doesn't get a degree, he will eventually find opportunities that are not available to him. There's no secret here in the Nuclear World different than any other: people without a degree eventually hit a "glass ceiling" in their careers. Keep in mind there are MM2 sailors that left the Navy in 2009 with not only a technical degree, but several courses into their Master's degree. As the 9/11 GI Bill gains momentum and colleges continue to offer more flexible, accredited engineering programs to young sailors, you have to consider what the Nuclear Industry will want and what the competition among job seekers will be in 2015, 2020, and beyond. I suspect that what worked for some of us "NukeWorker Dinosaurs" will not hold true in all cases in years to come.
Finally, I saw few Navy Nukes leave the Navy for Commercial Operations over the last 20+ years, although 2009 seems to be a banner year to change that statistic. A BSME or BSEE will provide a pathway to many non-nuclear opportunities. As I posted elsewhere here, non-nuclear companies do offer job interviews based on having a strong nuclear background as "we" seem to have a reputation for technical ability and hard work regardless of the circumstances. So, given that, I assume that is where your son is at...earning his reputation, finishing Boot Camp, A School, etc. He should start thinking about long-term academic goals now; however, he needs to be the best at what he's being asked to do now. If he doesn't obtain a Navy Nuclear NEC, then his nuclear career will be derailed.