The term and designation "RN", Registered Nurse, is a legal title and license to practice. The process is similar to getting a driver's license. You can take Driver's Ed, but until you take and pass a driving test with the state department of DMV, you cannot
legally drive. You can finish a nursing school program, but that doesn't
legally make you an LVN or RN until you take and pass the NCLEX no matter how many college degrees, diplomas or certificates from nursing schools you have. An RN license can only be granted to you
by the state not a school. Did you read your state board requirements to take the NCLEX? The school you are choosing to go to has met the requirements with the state board for their students
to take the NCLEX. If they or the state board haven't made it clear how this is accomplished, by a degree, diploma or
certificate of completion of some kind, call them up and ask them. LVN schools that are within community colleges train students for the NCLEX-PN all the time without granting an AA degree. But, they usually give the students some type of certificate for completing the course of training.
An AA (Associate of Arts) or BSN (Bachelor's in the Science of Nursing) are an honor bestowed upon students who meet the qualifications each college has specified for those levels of education completed and in those fields of study. Every college catalog describes the requirements needed to earn one of these degrees that the college offers. Many universities also have several "schools" within them, such as a school of arts, a school of science, a school of fine arts, etc. That is how they come to have BA's (Bachelor of Arts degrees), BS's (Bachelor of Science degrees), etc.
One of the things you should be doing is getting, or downloading, a copy of this college's official catalog and reading the information in it about degree and graduation requirements. There will also be a section in the catalog about the nursing program that will give specific information about it. You need to be reading it as this is considered to be the official word by the school about their program and degrees, diploma or certificates that they offer. If you still have questions, then call the nursing department of the school.
I have both an AA in nursing and a BSN from different colleges. In both cases prior to graduation, each college required that every student seeking graduation file a request for the degree with the office of the school granting the degrees. That office then pulls the student's transcripts and compares the list of all the courses the student has taken against the list of coursework that is required to obtain the degree the student is requesting. They send a letter to the student informing them if they are eligible and being placed on a list for the next scheduled graduation or they will inform them where they have deficiencies in class work required to get the degree they seek. This process is clearly spelled out in every college catalog along with degree requirements. Anyone can do this process informally by using information from the college catalog or meeting with a college counselor.
I just want to add that once you get into a college you are not just in nursing school. You are a college student and you need to be savvy about being a college student.
If you haven't read the information on how to become a nurse, you need to: