Correct, though it's hard to imagine he would use them all. He's already 20 years old; surely he would go pro before reaching age 24. I am not sure if he is draft eligible, but if he is he would have to consider going pro this June.
Does his having enrolled at FSU knock him out of this year's draft? He would've been an age-eligible sophomore in 2010 anyway, so I have to assume that is still an option, if not this June.
In past years, the White Sox would still have rights, but I think the new Aug. 15 deadline rule rules that out. I think if he wants to go ahead and turn pro he has to be drafted again.
I'm thinking he might find a Florida JuCo where he could step on the field immediately.