It doesn't matter for the most part, especially if you subsequently earn a BSN from an accredited school. I'm not sure how it would affect licensure in other states, as the myriad requirements are somewhat confusing. Some employers may prefer graduates from accredited programs. An example that immediately pops into mind is the Army Reserve which requires nurse corps candidates to have graduated from NLNAC-accredited programs or have BSNs. I haven't researched the intricacies of this as I graduated from an NLNAC-accredited school (and am now in a CCNE-accredited BSN program). Accreditation costs money and doesn't add any significant quality to the educational program, though it does imply that the accreditation standards are met. I recommend you consider individual program reputation, cost, and convenience in your school selection process.
I think the most important thing is that you get those two letters (RN) after your signature. Good luck.