When I checked this, as a fun experiment to do with kids (they love "winning" this game, after all), is that yes while I'm technically able to hear 15-16 kHz, there's a
very steep drop-off in sensitivity already quite a bit below that. I needed to turn up the volume on a pure sine-wave quite high (which the kids hated immediately) to be able to hear it somewhat clearly.
So if you add in ambient noise (in lower frequencies), that could plausibly drown out a 12 kHz noise very well, for older adults (I'm mid 30s myself).
Interesting side-note: Turns out that the low end drop-off (at about 20-25 Hz or so) is not very age-dependent at all (at least when I tested these "against" a 13-year old's hearing). You need quality headphones for this, most speakers will distort/resonate some higher frequency harmonics, which you can always clearly hear. It was very interesting to hear something that was clearly a very very low frequency tone turn into a sort of rapidly fluttering/beating sensation at the cross-over frequency, you can feel it beating slightly on your eardrums, but it doesn't translate into a "tone-like" sensation any more.
And yes we made sure to not do it for more than a few seconds, to not accidentally cause hearing damage--though with good closed headphones we didn't need to turn it that high, as the effect wasn't so much that the perception of the tone "disappeared", rather change into a different type of sensation.