With only eight picks in the first 10 rounds, the White Sox ran with college pitchers early on. College pitchers usually have some sort of innings governor after turning pro, but it's hardly a blanket policy.
Carson Fulmer, whose season just came to a close, threw 128 innings for Vanderbilt, which is the most NCAA innings thrown by a Sox draft pick over the last six years. Jace Fry comes closest, and he threw the second-fewest pro innings of the sample. I assume that will be the case here.
With the other two picked by the Sox, it's more difficult to ascertain.