I get pareidolia from white noise. Not a lot, but enough that the 'sounds' are more distracting than mundane background sounds like TV or music that I can tune out easily.
No but I've spent a good amount of time doing vaguely sound-engineering work where I listen carefully to audio samples. I may have overtrained some pattern-recognition wetware along the way.
Even 'naturally' generated white noise (e.g. Marpac Sound Machine)? I have similar problems listening to electronically generated white noise but no problems with the Marpac.
Possibly not lab-grade white noise, just broadband audio noise in general: fans, moving water, RF static, voice codec comfort noise turned up too loud, that sort of thing.