On iPhone, activating the microphone causes an icon to appear, which the app can’t hide. I think if the app is in the background, it turns the whole status bar bright red.
Secondly, there is power use attribution and it would be very obvious if an app were keeping the device awake and the microphone on based on battery drain and runtime accounting.
So you are asking us to accept on faith a shadowy ad SDK that is both widely used but also cannot be named, one that somehow subverts multiple layers of the system security architecture? Ok. We believe you.