Yes, every online record's dossier links to your website. Whether that link is a followed link depends on reciprocity: embed the ARCHIVE-9 badge on your site and the link is followed; remove the badge and it reverts to nofollow after a grace period. The Director checks daily.
An honest note: ARCHIVE-9 is a young archive, and we make no claims about what any single link does for your rankings. What you get is a permanent, crawlable dossier page, a followed link under the badge rule, and a directory that verifies its owners instead of listing impostors.