Yes, breadcrumbs affect SEO both directly and indirectly.
Directly: by adding correctly marked-up breadcrumbs (such as by using Schema.org), you are telling Google where on your site your content is found. So grouping articles by category is beneficial - you are reinforcing that you're not just writing a one-off piece, but you have a full category of related articles.
Indirectly: also by using correctly marked-up breadcrumbs, the way your site is listed in the SERPs will be a little different. Without breadcrumbs, your SERP contains the title linked to your page, followed by the URL of your page, followed by a description. With breadcrumbs, instead of showing the full long URL of your page (or Google truncating it with ...), Google will show your domain, followed by
> and then each breadcrumb. So visitors will see that you have a full category, and not have to read through the full long URL, making it a little more likely that they will pick your listing and click on your link versus a competitor's.