You'd want to contact a nursing advisor at MCI VA Beach to discuss your concerns. I'm happy to share my opinion, but I'm a nursing student, too. I'm still working on those critical thinking skills.
That said, MCI VA Beach nursing program would *have* to be accredited by the Virginia State Board of Nursing in order for their graduates to be able to sit for the NCLEX-RN exam. Can their grads sit for the NCLEX-RN exam? You could call the Virginia State Board of Nursing to find out. Their number is (804) 662-9909. Or, if you want to do your own research, you can check out their web page here:
The program may not be nationally accredited, nor would it need to be. National accreditation usually isn't an issue with employers, in my experience. They're looking for the RN licensure. If you continue your education, please be sure that your prerequisites and other courses outside of nursing are covered under institutional accreditation, and that your nursing program is nationally accredited by either the National League for Nursing Accrediting Commission (NLNAC) or the Commission on Collegiate Nursing Education (CCNE). If not, your credits may not transfer if you decide to continue on for grad school. You may want to contact RN to BSN programs that might interest you in the future, to see if they have articulation agreements, "deals", with the RN programs you're considering.
The community college program I'm attending for the RN is not nationally accredited, but I was told state accreditation is sufficient. The college itself is accredited by the North Central Association of Colleges and Schools. I'm not worried about accreditation. What is critical for me when choosing a program, or deciding to stay in a program, is the NCLEX pass rate - what percent of graduates get licensed? Another concern is the retention rate - what percent of nursing students graduate? I don't know your situation, so you'll have to do a self-assessment. This is just my two-cent opinion. Good luck to you.