Sort of? Here's the thing: The world is full of professional designers who spent hundreds of thousands of dollars on fancy design degrees. To a hammer, everything looks like a nail. Designers tend to think that everything has to be designed perfectly. I disagree.
Note: I want to be very clear that I'm talking about the aesthetic aspects of your website design. As soon as design starts impacting usability, then my answer changes to, "yes, design is the most important thing in the world."
Imagine a potential customer of yours is comparing you with some of your competitors by looking at your websites. What are the things that will matter to them? Maybe things like pricing, location, level of customer service, the quality of your product or service, etc. Do you really think they're going to buy an inferior product just because the website is designed well?
But that doesn't mean design doesn't matter at all. It has a major impact on first impressions. If someone comes to your site and they don't think it looks professional, they're going to wonder what else about you is unprofessional. It's just like how certain professionals wear suits to work. Sure, the suit has nothing to do with their ability to do their job, but it's the first thing other people see. A nice suit communicates, "if I'm competent enough to own this suit, get it dry-cleaned and tie my tie correctly, maybe I'm also good at other stuff."
Design is all about getting past the first impression. If the design is good enough, the customer will take the time to learn about the more important things like the quality of your product or service. If the design isn't good enough, they'll close the tab before even giving you a chance.
Almost everything I write on this website is explaining how to be "good enough". I run a small business. If you're reading this, it means you probably do to. People like us have too many things to do, and not enough time to do them. One of the keys to staying effective is to spend time on the most impactful thing possible, and that often means realizing when you've hit diminishing returns. Every discipline, whether it's design, writing, sales, marketing, or customer service, has an endless amount of room to continue improving. The best entrepreneurs pick one or two things to be amazing at, and they're just "good enough" at everything else.