CPU Speed Accelerator

It doesn't increase the speed of anything. What it does is change the task priority which forces the CPU to assign more time to the application before that task switcher moves to another task.

By default OS X launches user applications with the same priority meaning each running application gets the same amount of CPU attention. By increasing the priority of certain applications they get more CPU attention. This gives the impression that the application is running faster.

All that utility does is execute a Unix command (renice) that is used to reset the priority of any running task. It simply selects the foreground task and resets its task priority. Of course this also results in "slowing" the background tasks. You don't get something for nothing.

Re: battery life, yes it will decrease it dramatically. Unless you find you need the extra speed, I would personally recommend quitting using the app.