Well, it has happened to the Twins at least once since 2005. July 6th, 2007: Mike Redmond was catching, Joe Mauer was the DH, and Matt Garza was pitching. Jim Thome swung so hard, he ended up hitting and cutting Redmond's hand on the backswing. Mauer had to suit-up, and Garza had to bat in the eighth spot.
On July 7th, 2007, the sun rised, the birds whistled, the Twins and White Sox played another game, and life on Earth continued unabated.
So you can see why the possibility of pulling a catcher due to injury- with your other catcher as the team's DH- would worry Gardenhire so.