I think sounds can be musical. But music is more than sounds. There needs to be some information, some organized content, and possibly (but not necessarily) a rhythm or repeating pattern. There has to be a "this" versus "that" to communicate information. Ones and zeros. As opposed to a random or white noise content which has no information. There might be times where random or white noise is exactly what you want, but I'm just theorizing here. And I'm generalizing of course. But that, I think, is the main point to start this discussion from.
Here's an example. The percussionist in my band plays a guiro in our interpretation of Johnny Cash's "Big River". I keep telling him to play a repeating pattern, basically a zydeco washboard pattern. I'm playing a real simple one two one two thing, and the guiro fits nicely with that. But he tends to want to "solo" with it, where he starts playing on every sixteenth note. At that point, I think, what he's doing ceases to be a meaningful pattern of "information" and becomes noise. It clutters everything up, and doesn't add anything to the music. Problem is, as many times as I tell him this, he keeps going back to doing it. It totally bothers me, but bands are always a work in progress, so I'm dealing with it.
And now, telling that story makes me think of another question that fits into this discussion: when do sounds (music included) become noise? How's THAT for subjective?