Ni-MH + Cordless Tool >> Charging Dock
Your diagram suggests that you are going to parallel all four battery terminals on the charger and connect them to both the screwdriver and the battery simultaneously. This has a few problems:


You need a charger designed to charge a battery pack with the correct voltage and charge current. Since we don't know what the internal circuitry of your charger is (are they in series or parallel) we can't say if your one will work. e.g., It may internally have a 3 V power supply with current control to each battery. You won't be able to charge a 6 V pack with that.
Your charger will probably be overloaded if you use it to run the motor.