New NYC ADN Program Swedish Institute not accredited?

A new program just started. The first class was admitted in January. The school is NOT accredited by the National League of Nursing Accreditation Commission or any other nationally accredited commission. It's accredited by the state only. Does that mean those who graduate from the program cannot use their license in another state? Does it mean that those who graduate from the program cannot advance their studies toward a BSN since only those attending accredited nursing school programs qualify to attend other accredited schools to pursue advanced studies? Does anyone have any advice?