All of those sites have been around forever (in Internet time), and they all rake in tons of money, despite their lack of (indeed, willful indifference to) trendy design esthetics.
Someone mentioned drudgereport.com above. That's just plain black text on a white background. It has an Alexa rank of 130.
But many is not all. If they were designed to be beautiful as well as functional, they might well see a bump in transactions.
The reason they don't is either deliberate branding (Drudge, I'd guess) or incompetence (eBay), or because it's not obvious the bump in traffic would be worth the expense and time (Amazon.)
And also history. When you've been around as a brand for a decade or more, you don't need shiny.
But it's really not a good plan for a startup to have an ugly site now unless it's making some kind of ironic retro point about itself.
More people would visit, or people would just buy more when they were already visiting?
I find it amusing that some of the most popular sites are considered bad designs by people who think they have all the answers to web site design (at least, they're getting involved in this season's look), whereas the sites which apparently demonstrate good design are ugly, less pleasant to navigate, and harder to extract information from.
They might also see a drop. Existing users might be confused or upset and leave. The site's performance may suffer. Blind people might hate it. Bugs might surface. Tools might fail.