It's essentially just a balancing act and can go either way. It's not really affecting any 'flow' as you say, but more the feel/ambiance of a game. Say you are working on a game and currently it has no background music. If there is a long span between any sort of action when you are just running around, you would probably want to add something to fill that space because it might feel a bit boring just listening to your footsteps. If you are making some sort of action game, it could help with suspense to add in some heavy drum hit changes when something happens.
You could think of game music just like they do with movies. There are times when the music fits, and times when it doesn't.
For games such as Angry Birds and Doodle Jump, there is really no need to add music as it could feel a little distracting while you are concentrating.