After the cancelled games in Baltimore, the White Sox knew that they'd be coming up with a tough stretch of games for the second half of May. The Sox right now are in a stretch of 18 games in 17 days. Next week is the toughest part of the stretch. After Sunday's game the Sox play three games in Toronto. Then, they fly to Baltimore to play a doubleheader Thursday to make up the cancelled games. After they finish that, they fly to Houston for three games starting on Friday. That's enough to stretch any pitching staff to its limits. To deal with that, the Sox could be using seven starting pitchers next week.
The first pitcher added to the rotation is Hector Noesi. He gets the start on Memorial Day against the Blue Jays. Since making his first appearance out of the bullpen on May 11, he didn't make another appearance until the 21st. The Sox had mentioned that Noesi would get some random starts once Rodon was promoted to the rotation to provide some additional rest so this stretch of games is as good a time as any.
During the Friday night broadcast, Dan Hayes also mentioned another possible starter for next week -- Scott Carroll. Unless something changes, he may be getting his first start of the season during the doubleheader on Thursday against the Orioles. After starting the season at Charlotte, Carroll returned to the Sox when Matt Albers went on the 15-day DL. Carroll has been the primary long reliever for the Sox since his return. In 15⅓ innings, Carroll has put up an 2.35 ERA and 3.39 FIP although the 4.38 xFIP is a concern.
As for the possible candidates to appear as the 26th man, the most like candidate is probably Chris Beck. Beck, who was on the roster but didn't play after the suspended game on May 9, started on Friday. Erik Johnson pitched on Thursday night for Charlotte so is also a possibility as is surprise prospect Junior Guerra gets the start in Charlotte on Saturday.
One person who won't be back as the 26th man this week is Eric Surkamp. Surkamp was traded by the Sox yesterday to the Dodgers for pitcher (and former outfielder) Blake Smith. Smith was drafted in the second round in 2009 out of UC-Berkeley as an outfielder although he also pitched in 41 games including three starts over three years at Berkeley. Smith switched over to pitching full-time for the Dodgers during the 2013 season. This year at double-A Tulsa over 16⅔ innings, Smith has given up one home run, nine walks, and 16 strikeouts for a 1.62 ERA and 4.20 FIP.
Scouting material is pretty slim for Smith. He did pitch in the Arizona Fall League last year, so there's some limited data on BrooksBaseball.net. He's got a 93-ish mph fastball and curveball. Last year, when playing for Chattanooga, he faced the Birmingham Barons five times, so the Sox likely knew what they were getting.
As an aside, the Dodgers first round pick in 2009 converted from a pitcher to an outfielder and is now out of baseball.