There are two different issues with accreditation of proprietary voc/tech schools. One is the nursing accreditation, NLNAC or CCNE, and that is v. important in terms of your nursing future.
The other issue is general academic accreditation, and that's what determines whether courses completed at one school will be accepted for credit by another school. Most of the proprietary voc/tech schools are not accredited by the organizations that accredit "regular" colleges and universities, and that's why "regular" schools typically won't accept their courses for transfer credit. If you ask someone representing one of those schools if the school is accredited, they'll say "yes," and many prospective students don't know to inquire any further than that. However, most of those schools are accredited by one of the specialty organizations that only accredit proprietary voc/tech schools (yes, they created their own accreditation!). These schools are not held to the same academic standards as "regular" colleges and universities, and that's why the "regular" schools won't (in most cases, not all) give you credit for courses taken there.
If you are planning on furthering your education later on, that could create problems for you. ((Or even if you're not thinking about that now -- look at how many threads just on this site are about nurses returning to school for further education. Many, many nurses have had the experience of starting out thinking they want to do basic bedside nursing all their career, nothing else, and they will never go back to school again -- but, a few years down the road and with more experience in nursing, they start looking around and noticing how much wider a range of career opportunities and possibilities they would have with additional education, and they start to feel differently about that ...) IMO, it's a big mistake to close off any future educational and professional opportunities for yourself this early in the process -- but that's a decision for each individual to make for her/himself.
MCI is part of the ECPI College of Technology. The Virginia Beach campus of ECPI has regional accreditation through the Southern Association of Colleges and Schools. The other campuses of MCI/ECPI do not appear to have regional accreditation.
At my university, we do not accept students from nursing programs that are lacking both types of accreditation (nursing and regional).
If you are getting the BSN from MCI in Virginia Beach, you should be able to go on to do what you would like afterward. Commission on Colleges lists MCI-VB as fully accredited to award up to a Bachelor's degree, and SACS is the same group that accredits the major universities in the region. The NLNAC website lists the BSN program as accredited. If you have a question about whether the school you are interested in going to for a graduate program will take MCI's BSN, call or email the program directly.