Not on its current link. When you first publish a dashboard, you choose who can open its link: anyone with the link, members of your organization or only you. That setting is fixed for the life of the link. Publishing again adds revisions under the same link, with the same setting.
To change who can open the dashboard, revoke the link, then publish the dashboard again with the setting you want. That makes a new link with a new URL, and the old one stops opening, so send the new link to the people who should have it. Revoking deletes the revisions kept under the old link, and the new link starts from the revision you publish. A dashboard has one link at a time.
If you publish with a different setting from the one the link has, without revoking it first, Emolysis stops and says so before anything is uploaded. A new link is open to your organization unless you choose another setting. See who can see a shared dashboard and sharing dashboards.