I will apoligise in advance for going all heavy on you, but I find the question thoroughly fascinating.
This is something I've been thinking about a lot lately. The basic question was, am I a sound designer or a musician? The answer that I've come to is that they're actually the same thing. It's just a question of the metric you're working under. Music is the organization of sound with its nexus at harmony, dissonance, and tonality. Sound design is the organization of sound under the rubric of texture and harmonic structure.
I guess my argument is that there are so many points at which the two overlap - adding EQ and reverb to music, tuning sound design elements to fit with the key the score is written in - that you kind of can't differentiate between the two.
But it also to a degree depends on what kind of music/composition your talking about. I make mainly IDM-ish, aleatoric-ish, heavily sample-based music. So all of the sounds that I use I have made myself, and made to fit a particular part of a particular piece. I like doing thisSo, I'm good at itin short, yes.
On My sound design skillz do influence how I make music.
What I find so interesting about the question is how the two topics are related. If you look at the other side, the more "traditional composers" - I shudder to use the term - take already well established sounds and weave them into hitherto unheard configurations, something that I hate doing (probably because I'm bad at it).
For my own ears, I find myself more and more uninterested in music made with traditional physical instruments. To a great degree they have in my eyes become cliché (or perhaps I'm just a disenfranchised, jaded, sound snob. Who knows?). However, to many people the what-the-hell-is-that-godawful-racket music that I make is, well... a godawful racket. So who knows? It really depends on the scale by which you measure your sounds.
I have come to the conclusion that simple musical composition - i.e. composing music for established sounds: oboe, flute, guitar, drums, piano, &tc. - is really macro sound design. It's kind of like the relationship of chemistry and biology to quantum physics. Chemistry and biology are in effect macro-quantum physics, the study and manipulation of the effects of quantum interactions. By the same token music is the manipulation of quantum-aural interactions. Sound designers manipulate the wobbling strings on the micro level that give shape to the atoms which composers combine into complex musical molecules on the macro level.
However, I don't think that that necessarily implies any kind of value judgement (which I really don't want to be construed as making here). Sound Design is not any more deep, complex, subtle, moving, and intense than Macro-aural music composition, they're just different angles of looking at the same thing.