It really depends on your career plans...
It really depends on your Navy experience...
It really depends on the whole package...
Why such a vague answer? Because there is no set answer for your question. SInce leaving the Navy, I have been offered jobs by federal and private companies to be a SRO-trainee, Health Physicist (not tech, but a professional HP), and a Chemist.
All these jobs had a base salary between 58-68K and included the full bene package and RELO. Do I have an engineering degree? NO. Am I a ABHP certified HP? NO. Do I have a degree in Chemistry? NO. Do I have a degree? Yes. A BA in Liberal Arts from Thomas Edision State College.
So that should answer at least one concern? The most important thing is HAVING a degree from an ACCREDITED institution of higher learning and TESC satisfies that 100%.
However, let's look at the whole package concept. How many years have you served? What supervisory roles have you held? Awards? Instructor duty? Qualifications?
I have pretty much been playing up on my Leading ELT and Instructor qualifications and overall history of sustained superior performance and all that to gain entry into the civilian world of chemistry and HP.
But, I have 4 different resumes, pinpointing and playing up certain skills depending on the type of job. The degree is always included and when asked why a tech guy like me did not get a tech degree I always say:
"I have nearly 10 years of technical experience in applied engineering; although getting a technical degree would have seemed a natural fit, I wanted to explore other subjects to give me a wider breadth of knowledge"
That hasn't seemed to hurt me so far, and my ability to communicate on a human level (think nuke, speak human) has proved to be exceptionally useful in competing for jobs.
I am not saying don't get the BSAST, because its very prevalent in the Navy Nuke turned Civilian Operator ranks, just get a degree that you desire based on your interests. Its just a BS/BA, get it, and prepare for MS/MA degree.
Overall its the whole package: Your resume, you experience, how you present yourself in person, your ability to effectively verbally communicate, your education, how soon you send back Thank You cards to the people interviewing you (LOL). Everything.
And the QAI? It doesn't hurt. Quality is huge in and out of nuke land.
Let me know if I can be of futher assistance.
Good luck and thanks for you service.
JMK