

The short answer is yes, no, and it’s complicated.
If you are a fiction writer, you can get away without a platform if you write the very best fiction you can. People who love your type of fiction will (eventually) find your book. When they do, they will tell others. More importantly, once a reader loves your first book, they will be highly receptive to the idea of buying your next one.
That said, there are a number of genres where a niche platform can be highly effective. One of the best examples is Andy Weir. Weir spent 10 years building a following of dedicated science fiction lovers who enjoyed his story as he published and refined it. This translated into a book and movie deal and gave us The Martian starring Matt Damon.
For non-fiction writers, a platform is essential. Your sales will be entirely based on your presence as a known domain expert. That is someone who knows what they are talking about in the field they wish to publish within.
For experts, established credibility is everything.
This is why fiction authors can often do well “without a platform” because their existing books pretty much are their platform. This is also why non-fiction authors need a platform.
Writer Seth Godin has written and sold many excellent books on marketing, but he did not do so in a vacuum. Godin established himself first by living what he would later write about. Godin co-founded Yoyodyne with Mark Hurst and later sold it to Yahoo, where he worked as a director of marketing. Then Godin started Squidoo, which he later sold as well.
Additionally, Godin writes a blog with regular digestible posts that are easy to read, easy to understand, and readily inspire marketers. Some of Godin’s book ideas started as blog posts.
With a reputation for knowing what he is talking about and a body of work to demonstrate his standing, Godin has a powerful platform that sells his books in droves.
That depends. I would say that it never hurts to have a home base on the Internet that interested people can go to. Even if that is a pretty but static site where journalists can look up more information, there are links to your books, and a photo or two. Having a website is, unless you really mess it up, better than not having one.