Some people immediately reply, "Yes!" to that question, the same way people shout "Yes!" when asked whether a painter has to be able to paint recognizable objects before being able to paint abstractly. "Know the rules before you break them," is common advice to artists of all kinds.
Does that make sense? Why should an artist's ability in one mode be a determiner or critique of the artist's ability in another mode? Does the fact that somebody can "write a good, old-fashioned story" make you like their experiments any more than you would otherwise? Plenty of people write bad stories with "the rules", so why is it worse when people write bad stories without them?
I can think of a few visual artists who moved from representative painting to abstract -- Picasso being the most obvious. Is there a literary equivalent? No-one springs immediately to mind, perhaps because of my own ignorance (I haven't read, for instance, the earliest works of William S. Burroughs and John Barth, who may fit that pattern, but I'm only familiar with their later, more famous and experimental books).
I can't begin to get close to Jeff's question, because others nag me: Whose definition of experimental are we using here? Isn't every piece of writing an experiment of some sort, one that could be a success or failure? Whose definition of "good" and "story" and "good story" are we using? What period of history? What culture?
"Experimental" is, like so many labels applied to fiction, prone to problems, quibbles, and questionable assumptions. Plenty of writers prefer the term "innovative", but that just exchanges one vine of semantic thorns for another. Where the line between "traditional" and "experimental" lies depends on who is drawing it.
This does not mean that I deny there is such as thing as "experimental" or "innovative" writing, any more than I deny there is something called "science fiction", despite the fact that everyone has a different definition for it.
Nor do I deny that lots of writing that seeks to be innovative and edgy is utterly awful -- lazy, imprecise, meretricious, tedious, and stupid. It's difficult to criticize such writing, because it seeks to create its own rules -- rules that may or may not be apparent to the reader. What sometimes gets forgotten in the arguing back and forth between traditionalists and mad scientists is that just because a piece of writing scorns familiar literary customs and conventions doesn't mean that it exists without its own customs and conventions. It is against those customs and conventions that the work can be analyzed and evaluated. The burden lies in the work itself, for it must offer some clues as to how it can be constructed in the reader's mind. Even Finnegan's Wake, one of the most obviously experimental books in English, follows a system that can be interpreted, and (with some work) readers can judge for themselves how much the book's goals are ones they are sympathetic to, and how well they think it meets them.
Joyce himself may seem to be a writer who started out writing traditional stories (in Dubliners and the play Exiles) and who, with each book, moved farther and farther away from the basic traditions of fiction. However, it may be easy to forget how strange Joyce's first stories seemed when he wrote them, because their influence on later work has been profound. (Exiles is different because it did not have much, if any, influence on later playwrights. It attempted to bring Ibsenism to the UK, but Bernard Shaw had already assimilated and expanded Ibsen's innovations, and Ibsen's own plays were quite popular.)
What about another Irishman (and friend of Joyce) Samuel Beckett? Even his earliest work is wildly experimental, and it just got more so with each decade, until his last pieces of prose and his last plays seem to be trying to silence themselves. He certainly doesn't appeal to all tastes, but to me Beckett is the greatest playwright and fictioneer of the 20th Century, a writer whose words I cherish, whose images haunt me. A storyteller? No, not really. And yes, certainly, at times at least. I don't know. The question seems irrelevant with Beckett. Should we throw Beckett away because he didn't, and probably couldn't, simply "tell a good story"?
Virginia Woolf, who began as a more-or-less traditional novelist (with The Voyage Out), seems to fit the model Jeff is talking about, because she was someone who was capable of writing fiction that used the conventions of the basic fiction of her time. However, she didn't write anything particularly interesting or compelling until she discovered new forms and structures that let her talents create fictions quite different from the standard fictions of her day. Her first two books are hardly "good stories" -- they're quite dull, actually. But they are stories.
In our own time, we have writers like David Foster Wallace and Carole Maso. I think Wallace is over-rated, with his fans so determined to call him a genius that his occasional good work gets lost in the hype. Maso is, it seems to me, a far more versatile and profound writer than Wallace, though she also, like any writer, has better and worse pieces of work. I'm fond of her collection of essays Break Every Rule, and will conclude these unconcluded stabs at thought with a passage from her essay "Notes of a Lyric Artist Working in Prose":
To use all and everything that is available to us through observation, memory, fantasy, desire, imagination -- so as to get up close next to one's vision.
Miracles might occur.
Jean-Luc Godard: "Cinema is not a series of abstract ideas but rather the phrasing of moments."
New definitions of story and character may be required. To imagine story as a blooming flower or a series of blossomings. To change the narrative drive, to better mimic one's own realities, drives. So that narrative might be many things. One hundred love letters, written by hand.
Understand and accept the limitations and contours of traditional narrative. ...
How to incorporate the joys and pleasures, tenderness, delicacies, the generosities and seductions of the novel and its narrative capacities with the extraordinary, awesome capabilities of poetry? There's the challenge. Who is up to it? I wonder.