If I remove the PS3 controller's battery and plug the controller in via USB, will the PS3 controller still function?

No, least pretty sure. I had a battery go bad. Would work with the USB for awhile but must have completely gone out at some point because it stopped working altogether.

Why would you want to remove the battery? Also I didn't even know that was possible.

Because the battery will die and leak battery acid? I'm wondering if plugging the controller in without a battery will still feed power to the controller.

@mikeyz: Like laptops, a battery is required in order to function properly; and all batteries for electronics come with chargers.