GOOSEGG, one of the best posts I've read in a long time. One thing that I will add is that players that are drafted can, and do, negotiate away the scholarship option. At least, that's what one of son's teammates parents swears he did.
The scholarship program also does not apply if your son signs as an undrafted free agent.
On a related note, some schools have a scholarship program that will pay tuition, room and board to help former athletes complete their degrees. After 4 years of baseball, son was one class short of completing his ME degree. His school's program paid EVERYTHING, tuition, room, and board, for him to come back and complete that final semester/class. (He took a "full time" schedule, even though he only needed the one class.)