The microphone isn't powered, so there's no way to do something as direct as you're asking for. A light indicating that it's "listening" would necessarily have to be controlled by software at some level.
It turns out the microphone modules used in smartphones have integrated preamp and ADC circuitry which needs to be powered.
This makes a lot of sense as mobile phones are an extremely hostile RF environment. If it were any other way, the phone's sound inputs would be flooded with that iconic "cell phone interference" sound.
