My belief is that this defines them as employees, and as such they can form a union.

Division III universities do not grant any athletic scholarships. They can receive other types of scholarships (e.g., scholarships for kinesiology majors), but I wouldn't call any of those recipients "employees."

Also employees?

Academic scholarships are generally given to attract high quality students for the purpose of raising or maintaining the colleges academic credentials.

Sports are not part of the academic curriculum. They are completely independent from the academics, except for degrees in things like physical education, or sports medicine.
I can't imagine academic students needing a union.
Also, athletic scholarships are not generally given for academic purposes, at least not in colleges that want sports to be a major part of their college brand.
Granted there are some schools where that straddle the two, and attempt to maintain the student athlete concept, but I don't believe this is what we are referring to here.
The reality of the situation is that any college with a strong presence in college sports is giving scholarships to athletes for their athletic prowess only.
These are the ones where it's evident that the student athlete is really an athlete that is also registered as a student. It's an illusion that they are at the school for any other purpose than sports.
If these athletes want to form a union, I'm all for it.

Passing grades are a requirement by their employers, so they need to be compensated