A lot of softwares can turn a cellphone into a microphone bug. However, it has to be installed on the cellphone.
The battery is still providing power to the cell phone. With the help of the telephone operator, who can access the Application Protocol Data Unit (packets sent to the SIM card), it can still be activated.
No battery, no power, no signal, no spying.
In my fridge ← Snowden
Note : you can't remove your iPhone battery