No.  You can charge the battery and have your Z1 or Z2 in the PowerShell and see where the charge is in the cycle, by viewing the battery icon.  When it displays 4 solid black bars, it is 100% charged.  You can also charge your battery in your PowerShell without having your Z1 or Z2 in the shell.

The battery WILL NOT charge if the Z1™ or Z2™ is providing treatment (blowing air) even if the PowerShell™ is connected to the power supply. 

You cannot use your Z1 or Z2 and charge the battery at the same time.  If you are using your device in the PowerShell with the Battery plugged into a wall outlet, the battery is NOT charging.