no...certain schools have "cross-town affiliations" meaning that students from more than one school are able to participate in one NROTC program. An example is WSU and Idaho State University...both schools are within a few miles of each other and the mids from WSU go over to Idaho for their NROTC activities. Not sure how common this is, but you should be able to find out if a particular school is affiliated with an NROTC program. Aside from these cases, however, generally you can't attend a school that doesn't officially have an NROTC program. For example, I looked into Embry Riddle at Prescott, AZ and they have no NROTC program, so I had to go elsewhere.
Anyways, hope that helps...maybe some cross town folks can chime in who know more about this.