You're not pattern matching all auto-generated audio. You are pattern matching the audio generated by a specific algorithm. An attacker who has access to your microphone will know which laptop you have and what hardware it has.
This assumes an attacker is targeting you specifically since otherwise this is all moot (a broad attack could care less as to why your microphone is off).
You wouldn't be using a PRNG for this, because what would be the point? The idea would be to generate some plausible-sounding audio, not garbage that a listener would obviously know isn't real.
Really, though, in general there's just no point to this altogether; just cutting power/data to the mic is fine. There's no need to attempt to fool someone with fake audio, outside of some very edge-case scenarios that I'm sure Dell (rightly) does not care about.
This assumes an attacker is targeting you specifically since otherwise this is all moot (a broad attack could care less as to why your microphone is off).