This battery is only for the buttons right? the Pen still working even with out battery?!
I doubt that the pen will continue to work after the battery is dead. It's bluetooth based so once the battery dies, the pen completely dies. Also, speaking of 'buttons', there is actually one more battery at the back so you have 2 batteries in total.
As far as I understand it.. and I could be wrong. The inking isn't bluetooth, it's an active interaction with the actual screen. .. but I guess to test try turning off bluetooth on the SP3 and see if you can still ink ;-)Actually 3 batteries. There are two button batteries for the top push button to work via Bluetooth plus the AAAA battery for writing. If the AAAA goes dead, you can't ink anymore.
As far as I understand it.. and I could be wrong. The inking isn't bluetooth, it's an active interaction with the actual screen. .. but I guess to test try turning off bluetooth on the SP3 and see if you can still ink ;-)