Cleveland is 5.5 games back, and currently also the first team out of the wild card standings, so the team has essentially a 5.5 game lead on TWO playoff spots. If somehow Cleveland was to pass the Sox, they would also need to have both Boston (2.5 game lead) and Houston (4 game lead) also pass the White Sox pace for them to not be a playoff team. If both Houston and Boston were to fall off, and Cleveland win the ALC, Toronto is the next team back at 7 games behind the Sox, and it only gets deeper for the trailing teams.
As of now it would take a LOT of things not only going back for Chicago, but also going right for at least 3 other teams for the Sox to not make the playoffs.