Yes, both SDSU and NDSU teams are eligible for the NIT. The SDSU women and the Bison men would both like to make that field. With all the "name" teams the Jacks have beaten, I would think their women have a very good chance. The Bison men have played a lot of "names" very tough, but lost. They may still have a chance.
You are correct - this is something that UND teams could strive for during the first few years.