To a certain degree it is something to consider, however, its also important to determine where you plan on going career wise. Myself I plan on continuing on for my B.S.N, which will then make the issue of accreditation rather mute.
I researched this issue, when applying to the school I chose. There were only a few considerations. First the well known, you won't be able to work for the military or a VA facility. NLN accredits primarily community colleges, it is the recognized accrediting body for the Department of Education. I believe the CCNE accredits four year schools. The one concern I had, and decided that I can overcome it by completing my B.S.N, is the endorsement of a license in another state, most states don't really care if the school has the NLN or CCNE, so long as the program is approved by the states Board of Nursing. However there is one exception that I checked into, and its fairly vague. That is in California, since I plan on moving to the Bay area in a few years, this may or may not be a concern. Again it all depends on what your career goals are at present. Personally I decided that it was not worth omitting a school that has a fairly decent success rate. There are many variables that could prevent a school from obtaining a particular accreditation. Ultimately, it comes down to evaluating the program, its success rate, and employability of its graduates. Those were the factors I considered. Just my thoughts, hope this helps.