My understanding is that it does not. Yes, we can hear a louder sound at a greater distance. However the percent attenuation is the same for loud sounds and for soft sounds. If we are at a great distance from the source of the sound, the sound waves from the softer sound may have dipped below our perceptual threshold. Caveat: My background is in chemistry, rather than physics.
Loud and soft sounds attenuate at the same rate, but human perception of sound will vary according to hearing thresholds.
An interesting story: I once did a quick listening check on my son's hearing aids in the car, and heard a man speaking softly. This sort of freaked me out, because I couldn't figure out why there would be the sound of a voice in his hearing aids when there was no one else in the car with us. As it turns out, I had the radio turned down so low I couldn't hear it (I thought it was off), but the amplification on my son's aids made the (very) soft sound perceptible to my ears. Took me a few minutes to figure that one out!