She would have stayed in London, dined out, lunched out, met famous people, made new friends, read, travelled, and carried back to the quiet country cottage a hoard of observations to feast upon at leisure. And what effect would all this have had upon the six novels that Jane Austen did not write? She would not have written of crime, of passion, or of adventure. She would not have been rushed by the importunity of publishers or the Battery of friends into slovenliness or insincerity. But she would have known more. Her sense of security would have been shaken. Her comedy would have suffered. She would have trusted less (this is already perceptible in Persuasion) to dialogue and more to reflection to give us a knowledge of her characters. Those marvelous little speeches which sum up in a few minutes' chatter all that we need in order to know an Admiral Croft or a Mrs. Musgrove forever, that shorthand, hit-or-miss method which contains chapters of analysis and psychology, would have become too crude to hold all that she now perceived of the complexity of human nature. She would have devised a method, clear and composed as ever, but deeper and more suggestive, for conveying not only what people say, but what they leave unsaid; not only what they are, but (if we may be pardoned the vagueness of the expression) what life is. She would have stood further away from her characters, and seen them more as a group, less as individuals. Her satire, while it played less incessantly, would have been more stringent and severe. She would have been the forerunner of Henry James and of Proust—but enough. Vain are these speculations: she died “just as she was beginning to feel confidence in her own success.”
It's dangerous to disagree with Woolf on a matter of writing, but I think she is partly misled here by her reading of Persuasion and by the error of thinking that dining in London and meeting famous people is much of a way to gain a new appreciation for the complexities of human nature. While Woolf does have some interesting and plausible things to say about Persuasion if read as a transitional book, which it certainly is, a number of features Woolf attributes to Persuasion are found much earlier; and some of the harshness of the work, assuming it is not due to the fact that Austen never had time to put a final polish on it, is due to the fact that Persuasion, more than the other books, is about how human beings can be a detriment, intentionally or unintentionally, to other human beings.
When we look at Sanditon, the unfinished novel, we find that the satire is indeed more stringent and severe -- but it is in fact more incessant, becoming a sort of subtle atmosphere. I do think it likely that Woolf is right about Austen trusting less to dialogue and using the suggestive more, since this seems to be something of a trend within The Six themselves. But all the signs are that this makes Austen more satirical, not less. There seems to be another trend in her heroines, a trend toward more intense virtue; or, perhaps, it would be better to call it 'sophistication of virtue'. And, with all respect to Woolf, the kind of people one meets when dining and lunching out and meeting famous people and staying in London show up worse, not better, against such a heroine. We see this in Sanditon, as well, for all that we get only a very limited glimpse of the heroine; she seems on the way to being a wittier Anne, and everyone looks even more ridiculous in comparison, because she sees through them. It makes her the perfect heroine for a work that looks like it would probably have been, among other things, a commentary on the moral hypochondria and convalescence of the day -- that is, on excuses for not doing the right and sensible thing. And this is almost certainly what Austen would have seen in Woolf's scenario: more excuses, more hypocrisies, more superficialities masquerading as sophistications. It does seem that as The Six progress we get more of a sense of people in groups, so it's likely Woolf is right that this would continue; but the result, contrary to Woolf's suggestion, is more individuality, not less. By seeing them in groups, Austen sees more of the heart of each character, not less.
An Austen novel about London would be worth reading; and all indications are that such a novel would be harsh, ruthless, and devastating. But even that, of course, assumes that Austen would have found London interesting enough to write about; she might well not have. She spent time at Bath and in the novels we only occasionally get there; Austen as we know her likes more scenery and less artificiality than that. Bath ends up being a contrast to human nature, or a device for mixing things that wouldn't ordinarily be mixed. There's no reason to think London would have been different. And I think Sanditon shows us that she would probably have gone a different direction even if she wanted to write about London. Londoners in their native habitat can hide their quirks, or pass them off as reason; get them into new situations, let their fads and fashions carry them out of their element, and that is where an author like Austen would give us her telling of what London is. And the danger of it is that there might not be a novel's worth there. While Woolf, no doubt, would give us an excellent account of London that explores subtleties too nuanced for a hit-and-miss method, Austen herself might well have found it precisely the sort of thing to sum up in a few devastating lines and dismiss forever.