MLB pays for education, with some wrinkles not relevant here. The biggest hurdle to your idea from the education side (leaving aside the effect of the CBA on HS picks), is Harvard will not leave the offer of admission open-ended. While Harvard will allow a student to defer matriculation (called a gap year) for a year - or even two - the offer of admission will not be open-ended. (At least that is the case with one of Harvard's peers in the case of the MLB draft.).
One other note: the Ivy's athletic recruits go through admissions to get in. As a 2014, there can be no slacking in grades or scores.