Does the blog/website address we add on various sites like Facebook count as a backlink in the eyes of search engines, especially Google?
All external links pointing to your site are backlinks (also called inbound links or incoming links).
Several backlinks have a positive effect for SEO and others don't. Backlinks with the
rel="nofollow" attribute or non reachable for Google bots or from a non-indexed page by Google have in general no impact for SEO.
However, even if backlinks from Facebook or Twitter have the
rel="nofollow" attribute, they can easily generate direct traffic for your site. Don't forget the only goal of SEO is to generate more traffic.
Moreover, communicating about your site with Facebook and Twitter can improve SEO because Google takes into account likes, shares, tweets, etc.