Sure, this would block the incoming/outgoing signal. But last time I checked you can still hear your surroundings when inside a Faraday cage/bag. So unless you plan on permanently storing that phone in a bag I can't see how this would prevent a potential recording from eventually getting out.

Just to check:

Some people are saying that mobile phones have a second secret battery, and that battery is used to power the phone to record anything the microphone can hear, and then later when the phone has a signal and normal battery power that recording is secretly sent out to some secret spy agency?