Trying to build a white noise microphone blocker

No, as far as I remember, I simply did a test connecting some head phones via a resistor or maybe a low pass filter (with the simple addition of a capacitor) to the Arduino pin while running the sketch. There was definitely no DAC involved. You can also add a simple high pass filter if you are concerned about non-audible sound pollution affecting dogs etc.
An Arduino pin can tolerate max ~40 mA

But that is as far as I got with this experiment although I don't rule out returning to it later.

I'd imagine that a sound source very close to the phone (or in direct contact with it) would not have to be very intense to block the microphone(s).