Or rather, what separates a writer from a non-writer?
Is it a matter of "being," some difference in essence? If so, publishing isn't a factor. If there is an essential, inherent difference that makes one a writer, then publishing is superfluous.
Is it a matter of "doing," a matter of practice and work? Again, if so, publishing is superfluous. A grad student does a lot of writing, with a lot of pressure (and for me, it was with the obsessive revising and attention to detail that I would expect from a published writer).
What separates a writer from a non-writer?