Yes, the design of your website has much influence in returning traffic. Design are not considered by the search engines, instead, search bots are looking at your content. Sometimes bots may read your scripts as well. But when it comes to a real person or visitor to your blog design will have a great role.
Whatever content you have may not be useful if your site's design is so boring and difficult to navigate through. Your page may have that content for the visitor but if a user is not able to find the exact content he searches on your blog the what is the purpose of having such a blog. A badly designed website will result in higher bounce rate. Thus your blog traffic will decrease day by day.
A better design mean not only the appearance but also a design that constitutes faster page loads. A slow loading page also increases your page's bounce rate and will affect your blog's SEO very badly. So always try to start with a faster loading, well optimized, attractive and user-friendly design for your website or blog for better organic traffic.
You can check your page speed on this awesome tool from Google. https://testmysite.thinkwithgoogle.com/