It's a good question. Carroll is not a pitcher that I followed closely. The righty has never played in the majors and is 29 years old. That's generally all you need to know about a minor league player to safely assume you can not care about him.
The White Sox, however, are in a bit of a unique position. They've already delved two-deep into their minor league starting pitcher depth, with Andre Rienzo and Charlie Leesman both getting starts in the past week.
Rienzo is probably the near-to-medium term replacement for Felipe Paulino. Leesman was really bad - which shouldn't be a surprise considering he's a lefty who has trouble getting righties out - and, whether out of lack of merit or the desire to bring Gordon Beckham back without sacrificing a position player, he's not getting a second chance.
Chris Beck arguably would have been a few names down on the shortlist going into the season but his paucity of strikeouts, most particularly this season in Double-A, certainly makes one question whether he can handle Triple-A hitters now, let alone major league ones. Dylan Axelrod is Dylan Axelrod.
So a 29-year-old is getting his major league debut. What are his chances of success?
Pretty low. Carroll is a pitch-to-contact, low strikeout rate, meh walk rate pitcher. He has always done a good job of keeping the ball on the ground. His repertoire is pretty unremarkable. As you'd expect from a guy who gets grounders, he throws his sinker a lot. His other fastball is the classic four-seamer. Both are 90 MPHish. His breaking ball is a slow curve and his off-speed pitch looks like a splitter to me. He probably can throw a slider, too.
He's not going to get many whiffs; the question is whether the hits will be mostly on the ground and/or right at defenders. If he gets some luck from the God of BABIP, he might be able to get through the Rays order a couple times relatively unscathed and pitch 5+ innings. Might.
Carroll does have an interesting background. Out of Missouri high school, he was more highly regarded than fellow Missourian Max Scherzer in the leadup to the 2003 draft. (Yes, you read that correctly.) Both of them had solid college commits, though, with Carroll's coming in the form of being a Purdue quarterback recruit. Quarterbacking at Purdue didn't work out so he transferred to Missouri State where it did. They also let him play baseball.
A third round pick of the Reds in 2007, he was unremarkable in the minors. The White Sox picked him up during the 2012 season. He blew out his elbow in the Venezuelan Winter League the following offseason. A lot of guys would have given up the ghost after that but he was back on the mound in eight months. Carroll wrote about the TJS rehab experience here.
If nothing else, his is a good story to tell before and during the game. We'll see whether the game itself will be a good story, too.