D-III's vary; some recruit players, and guarantee them a roster spot (about all they can offer as no baseball scholly's), others give no guarantees. Some recruit a ton of players to come and try out, while others recruit what they want, then have open tryouts, but the number of players making it through open tryouts is pretty small.
All D-III's have tryouts, but the track record for true non-recruited players varies from school to school.
With D-III's, it's a very very good idea to do your homework and inquire of existing players as to how things work.