Gimenez arrives in camp after missing the first three days because of visa issues in his native Venezuela. Dunn, whose wife gave birth to a daughter last month, is on hand two days before position players are required to report.
Missing days wasn't the best scenario for Gimenez, who is in a battle for the backup catcher role with Bryan Anderson and Josh Phegley. But it doesn't seem as if manager Robin Ventura will hold the late arrival against him.
"It's a long spring training, and he was playing winter ball," Ventura said. "It's not like he wasn't in shape or not doing anything or didn't want to be here. You get him in here, get him in the fold and he looks like he's been here the whole time."
While Dunn is just one of two left-handed bats in the projected starting lineup, Gimenez, a switch hitter, could give a left-handed hitting presence when Tyler Flowers needs a day off. Anderson bats from the left side, while Phegley is a right-handed hitter.
Gimenez, 30, has played in just 11 career games, and combined with Flowers, the White Sox's projected catching duo has just 119 combined games of experience.
"Last year, him coming up at the end of the year, you get a good view of what he can do," Ventura said. "He has quality at-bats, he knows how to play, he's a good receiver behind the plate. That's something that's really showed last year."