Can someone be considered a significant philosopher if they have not published a written work?

Only if the ideas are recorded in such a way that people can consider and ponder the ideas. So, a recording of a talk would be okay. But not just the speech of someone on a street corner without a way for anyone to share it.

I am going to assume that the question is restricted to contemporary philosophy since you probably already know that Socrates, who is one of the most significant Western philosophers of all time, was illiterate and never wrote down a single word of his philosophical thought.

In any case, Saul Kripke has certainly managed to become a very influential and significant philosopher despite having published virtually none of his work. Even his most famous book, Naming and Necessity, is just a transcript of three lectures he gave at Princeton a decade before it was published.

The book is actually very typical of how his ideas have managed to circulate: other philosophers share recordings of his lectures and copies of unpublished manuscripts, then cite those unpublished works in their own writings. And while it is true that his ideas exist in tangible form, they can actually be difficult to get hold of if you don’t know who to ask.

So while it is rare these days, I would say that the answer to your question is “yes.”

Of course, unless you mean “significant to publishing” or something.

Philosophical significance doesn’t require an audience.

If a philosopher goes to the forest and learns the secret to life, the universe and everything, then maybe everyone else is the philosophically insignificant one.

Consider Ringo Starr, setting Yellow Submarine aside, he didn’t write any of the Beatles lyrics & yet is thought of as one of the “fab four” philosophy by association…word!

This sort of gets to the questions of “what is philosophy?” and “who are the great philosophers?”.

Yogi Berra had a philosophy of life that was fairly simplistic and never written down.

Mother Theresa had a philosophy of faith and carried it out through service, but she wasn’t known for her writings.

Singer /poets like Phil Ochs, Bob Dylan, and the late Leonard Cohen have introduced us to their philosophies and views through their poetry and songs. But none of them have written a philosophical treatise along the lines of Rousseau or Kant.