Short answer, yes. Breadcrumbs add context to your pages, which help decrease your bounce rate (among other things), which negatively impacts your SEO, in turn, negatively affecting your SERPs. Search engines love breadcrumbs because it helps them relate one page to another. This is why you love breadcrumbs. Breadcrumbs help search engines discover and find relation in your innermost pages, then those deep pages will rank and you'll gain even more organic visitors.