If Shaq decides for football and to not sign with the Red Sox, he is not draft-eligible until after his junior year to re-enter the draft.
With the new MLB draft slotting, teams have a certain amount to spend amongst the top 10 rounds. They can't go 'over the cap' for those ten rounds but if they can save money on one slotted recommendation for a particular round, they can then spread that money around to someone else in the top 10. For example, if pick #5 in the 1st round is slotted at $3 million but team A is able to sign #5 for $4 million, they can take that $1 million leftover and use it somewhere else in the top 10 rounds. So if they draft a high school player in round #2 and really want him to sign but the allotted slot recommendation for pick #35 is $2 million, they can offer $3 million instead to entice him to sign. They could also add more money but it would take away from their pool of money.
Now, for everybody AFTER the top 10 rounds, the bonus they get does not count against the cap of the top 10 rounds UNLESS that amount exceeds $100K. For this reason, you will see a lot of top high school prospects decide for college instead. It is also why you saw a lot of so-so, average, fringy kids, notably college juniors or seniors get taken in rounds that were usually used for a high school kid with a higher ceiling then his college counterpart.
So, it all depends on what the Red Sox can afford to offer Shaq Thompson, if they even have enough money to entice him to sign. With all of that said, Shaq's better option appears to be head to Washington and play for the Huskies and if he really likes baseball, re-enter the draft in 3 years. The education he would receive at Washington, I presume, would be better then getting a more then likely signing bonus of less then $100k.
Or I would like to go with the age old adage, who frickin knows.