Google's John Mueller confirmed on Twitter that content placed in the <aside> tag is treated similarly to other content on the page.
Mozilla defines the HTML <aside> element represents a section of the page with content connected tangentially to the rest, which could be considered separate from that content. These sections are often represented as sidebars or inserts. They often contain the definitions on the sidebars, such as definitions from the glossary; there may also be other types of information, such as related advertisements; the biography of the author; web applications; profile information or related links on the blog.
Forum discussion at Twitter.