If you think of distortion as a type of noise, then yes, you could say that if you start with a high amount of noise to begin with you are going to have a harder time, but not impossible, hearing low amplitude noise that's in addition to the original.
On the other hand, our ears are pretty good at recognizing differences, so that's why I'd say it's harder, but not impossible.
A bigger issue is the room acoustics, IMHO. Clean that up and you can hear a lot of things you could not hear before.