No, I wouldn't keep them if that were the case.
It is kind of strange, the white noise/hiss sound disappears at around 1-2 feet, but there is a whine (upper midrange?) that sounds like a pot on the stove if there is a little water on the bottom as it is heating up (at least on the newer flat eyes).
I just listened to it, and once I've tuned in on it, I am about 9' away when it starts to drop out of my perception.
However, if I an 9' away and listen for it, it takes around 30 seconds to find and confirm it. If I did not know it was there, I don't think it would find me (as in I would realize the noise was present) unless I was 6' or closer!. This is with nothing in the house running to make noise, and I live far from traffic noise.
It is probably not a bad amp in a normal application, but the horn can be merciless in its ability to project detail!
But as far as listening to music, I think I would need to be 6' out, with a pause of 30 seconds in the music, and no AC, fridge, etc, and to be trying to find a noise to notice!
So no, I don't think I would ever notice it listening to music at low to moderate levels!
This is in the same range as the noise servo motors make, and I was surprised in the lab I used to run that the servo motor noise (which came and went depending on the position the motor was in - these were coordinate measuring machines) bothered me, but two girls (one late 20's and other early 30's) could not even hear it until I pointed it out to them! My hearing has certainly deteriorated with age, but for whatever reason, it seems to have stayed pretty good in this particular frequency range (hearing tests confirm that). There may be some higher frequency component that younger ears might detect which I don't hear at all.