Yes! If you're more interested in just collecting characters, or you simply don't have time for turn by turn decisions, Auto-Play is a great option to make progress in the game. Auto-Play allows the game AI to control your team for you and also provides an opportunity to learn some strategy you never thought of!
You can turn on auto-play mode by tapping the 'Play' button at the top center right of the Battle screen. To turn off auto-play, tap the 'Pause' button found in the same location.
TIP: You can still target enemies during Auto-Play.