Much depends on which DIII college you are at. Some are followed closely by the scouting community, many are not followed at all. There is a very big difference between the highest level and lower levels of DIII.
I would think that most coaches would know when they have a player with professional ability. They should also know some area scouts that they can notify and someone in a summer leagues.
Also, be proactive if you truly believe you're a prospect. There are Tryouts you can attend. There are ways to find out who the scouts are that have your territory. Contact them, some might work you into their schedule. Obviously, your coach can help in this as well if he wants to. For sure I would talk to your coach and see if he thinks you are a pro prospect. You can't expect him to lie to scouts or summer collegiate teams.
There are not a lot of DIII players drafted, but there are some. Much easier if you happen to be a pitcher. The new CBA actually benefits all college players, especially seniors. Chances of an early round or big bonus aren't likely, unless your an extremely talented and hard throwing pitcher.