I was asked this question recently. I'm thinking about it. Yes and no. How's that for a definite answer. (My students, btw, frequently assert things like, "I am defiantly glad I moved here!" and "Survivor is defiantly the grandfather of all reality shows." Cough. Spell-check is not always your friend.)
Writing voice is like singing voice. You're born with the potential for a good voice, or not,
and you can't be taught to have the potential. But you can be taught to refine
and improve the potential voice. And I think that even if you haven't the
potential for a good voice, you can certainly be taught to have an adequate
voice to suit most writing purposes. You won't end up singing at the Met if you
aren't born with the potential (and without insightful teachers along the
way!), but without the talent but with the teachers, you can learn enough that
you don't embarrass yourself at a group sing-along.
But yes, voice is more than just the rhythmic and
near-musical assemblage of words in a pleasing and/or effective pattern. Voice
includes worldview, attitude, personality, wisdom, and other personal traits
that exist within some of us, and can be brought into our writing to deepen
what we have as a voice. This is (to use another musical metaphor) probably
what separates (I'm dating myself here, but with Davy Jones's death, they're in
my mind) The Monkees (technically polished, even talented) from The Beatles
(ditto, but with some extra fillip of meaningfulness and imagination). The
Monkees couldn't help but be derivative, and The Beatles couldn't help but be a
thing beyond their influences. Now would you say that the depth and thought and all that is more or less useful than the technical expertise? Shallow-but-polished vs. insightful-but-a-mess. Well, we know, given that choice, what the buying public usually goes for.
I think "iimagination" is another aspect that takes voice above
the merely competent technically. I've taught former journalists who
really want to be novelists, and of course their writing mechanics are
admirable (they better be), but often they struggle to create characters and
stories that are beyond what they have observed. (Some journalists, often those
who struggled in their jobs with the desire to "just make it up,"
like, say Mark Twain, have great imaginations, but that's not really compatible
with the career choice.) They are often less successful as writers than that
fabulously imaginative but technically hopeless fantasist. You can hire
editors, but you can't hire imaginators.
But, as one who is somewhat imagination-deprived, I can attest that it's
indeed possible to go "deeper if not broader" when you don't have
much imagination, and still come up with books that are more than just
"what anyone could come up with."
Anyway, you can tell voice is something I'm intrigued by, and there! I ended
on a preposition! I feel sinful!