Well, one of the things people complain about with ATK is that while its running, the notification bar, home screens, etc are laggier. But really, this isn't a very valid complaint, as all you need to do is check the box for ATK to kill itself when you kill all, so I mean in reality there is almost no down side to this app at all. I have done quite a bit of testing with it as far as overall lag goes, and the only time it is slowed (and this is a very minor slow down) is when its active in the background.
In short, apps, active or in background, use resources. Resources use the battery. Therefor Apps use up battery life, even in the background. ATK ends apps, thus ending their usage of resources, thus extending your battery life.