No, the Z1 and Z2 do not require a battery to use.  If you purchase the PowerShell and battery, you can remove the Z1 and Z2 by pressing the two blue circles at the bottom of the PowerShell to release the device and use the Z1 or Z2 plugged directly into a wall outlet.   The Z1 and Z2 require either electricity or battery to power them.  The Z1 and Z2 cannot be run using the 12V DC power adapter.  The unit will switch off.