AParent:
In our experience, the term "recruited walk-on" never arose. An "invited walk-on" at UNC carries exactly the same status accorded your definition of "recruited walk-on." An "invited walk-on" gets a spot on the roster...works out with the team...no scholarship.
The term I'd apply to anyone below that status (someone attending the one-day tryout) in generous terms would be "hopeful."