As he i not on the 40 man roster, the Yankee have to add him quickly.
I doubt they do add him this season, as Cashman has been claiming and signing other bullpen alternatives. If the Yankees add another reliever to the 25 man roster, they have already put Ryan Dull on the 40 man roster. But David Hernandez should be the most likely of that bunch to actually see the post-season, IMO, as he has been the most effective in MLB this year. (I do expect Dull or David Hale to be DFA'd in this case.)
I doubt the Yankees give Garcia a trial by fire of MLB post-season baseball. Dellin Betances might even be more likely, assuming he has anything to offer right now.
Garcia will probably be in the bullpen mix next season as the replacemet for Betances. He might be fighting for a spot with Trevor Rosenthal...