Charging Magic Mouse 2 when the device is turned off… Simple question. 

Can I turn off my Magic Mouse 2 when I'm charging it's battery through the cable?
Yes, you can turn it off while charging.

However, according to Apple:


  For the fastest battery charging performance, be sure your device is
  switched on when connecting the Lightning to USB cable.


Source: Recharge the built-in battery in your Apple accessory