robba,
The only way to turn off this icon is by Right-Clicking on the icon and click Turn off System Icons, A Window will pop up and then you can have a choice to either turn it off or on, Meaning it will remain off when when you have your laptop on battery.
I don't think there is a way to have come on when the battery is on. and Turn off when you are not using the battery.
Hope this Helps...