It's possible. Say the Dodgers are playing the Giants, with the Giants one down on the Cards for the second wild card, and the Dodgers were one up on the Cards for the first wild card. If the Cards lose, then the Dodgers clinch the home WC game, and if the Dodgers then lose, the Giants and Cards would have to play a Monday play-in game in order to face the Dodgers on Tuesday. The Dodgers, if they knew this ahead of time, would have a huge advantage in losing the game. If all games are played at the same time, they would at least have to start playing to win.
There's other scenarios, I'm sure, that's just the first one I thought of.