Will your MacBook run off power only when battery is dead?
If your battery is dead and you connect the power supply with
your battery installed, the battery will automatically start
charging. If you wish to run your MacBook off your power supply
only, simply remove your battery from your MacBook and connect the
power supply. You will then be running solely on the power supply.
If you battery becomes fully charged while your power supply is
connected, you MacBook will switch to the power connector as it's
power source - preserving the battery.