Jesse Crain is scheduled to throw a bullpen session on Thursday as he tries to recover from his second oblique strain of the young season. Because his addition to the disabled list was made retroactive to April 21st, Crain is technically eligible to rejoin the roster as soon as this Sunday.
Even though he only missed 10 days this Spring for the same injury, that seems unlikely. Bruce Levine of ESPN Chicago mentioned that "a rehab outing or two is possible", which would certainly push the timeline beyond the next four days. While the bullpen could certainly use the return of a veteran presence to take some responsibility off of the shoulders of Hector Santiago and Nate Jones, there's a benefit to staggering it out until at least Monday.
The Sox are scheduled to make up April 10th's snowed-out game in Cleveland this coming Monday in a day-night doubleheader. There are no off-days in the schedule until May 10th, and any concern about pushing young Chris Sale's next start up a day goes double for Jake Peavy, who hasn't had good results when straying from normal pitching schedules, to say the least.
John Danks would be the one to make the start for the second game on Monday if the rotation continued unchanged, but if the White Sox opt for a spot starter--which seems to be expected--then the selection could be player up for demotion when Crain returns. Per the new CBA, teams can carry an extra player on the roster on the day of a doubleheader, which takes out long-term roster concerns from decisions centered around one day of play.
Dylan Axelrod had been the most impressive starter in AAA Charlotte when Crain was hurt, and has only been used once since being called up to replace him. Zach Stewart is similarly well-rested, started 8 games for the Sox last year, and originally beat out Axelrod for the last spot on the Opening Day roster.
However, if Crain's rehabilitation schedule is more protracted, and Stewart and Axelrod have more substantive bullpen roles lined out for them, the call could still come from Charlotte. As indicated in the linked-to Gonzales tweet, Eric Stults has been getting good results despite high walk totals, and Rule 5 Draft returnee Terry Doyle is available as well.
[EDIT: Per Daryl Van Schouwen of the Sun-Times, Axelrod is the likely spare starter for next Monday. So there]