There are plenty of opinions to be found on google. Most of those who say design matters are designers themselves. Most of those who say it doesn't matter are people profiling other "ugly" sites (plentyoffish, craigslist etc)
I think there's a difference between UX, UI and design (with large amounts of overlap). UX is the broad overall experience, UI is more specific as is concerned with how the site is used to complete various tasks and design is how it looks.
I'd like to hear from entrepreneurs who have launched their own successful sites. Does design matter?
I think you'll find that really good design (and designers) always think of their audience first. This isn't just a design mindset, but a marketing one. That thinking is essential to creating any good product from a website to a cooking wok.