Resetting CD4017 Counter when power source is OFF
No, pressing RESET while the circuit is off will do nothing as the chip is not powered up.

Holding RESET during power up is a different matter and will result in the circuit always powering up with Q0 on. If you don't hold RESET during power up you will get a random LED on every time.

To automate the reset you can add a capacitor - maybe 1 to 10 &mu;F across the RESET button. The result will be that when the power is switched on the capacitor will pull the reset pin high (+9 V) until the reset resistor pulls the pin down to zero by charging up the capacitor.