In the audio sense, the difference between "noise" and "music" (substitute "signal" for "music" if you prefer, or depending on context) occours principally in the mind, at least according to the modern musical school consisting of such people as Edgard Varese, John Cage, et al. Music had, up until the beginnings of the 20th Century, been defined, in a sort of un-written definition, as organized notes. This was replaced by Varese's definition of music is organized sound, which justified (in his mind, at least), the creation of the first all-percussion piece. Alvin Lucier ran with this and created the either hypnotic or irritating "I am Sitting in a Room", in which a spoken text is repeated over and over, until the harmonics of the room wipe out any semblance of recognizable speach. Perhaps the most telling experiment of the whole modern movement, however, is 4'33", in which the audience expects to hear music, but instead ends up listening to the ambient noise in the context of hearing music.
So what of it, then? If music is what is heard, then the difference between "music" and "noise" is not in the sound, but rather within our perception of the sound, and is infact largely determined by context--that is, when the brain knows that it's at a concert and is supposed to be listening for music, it is more likely to pick up on it, and therefore, even if the music is not what is expected, it is more likely to be interpreted something worthwhile. And therefore, in response to the earlier write up, I would say that yes, there is always signal in some shape or form, but context is often very important to obtain it.