Particularly, we wish to possess a Blogroll wordpress plugin around the Wordpress page, but obtain that also appear online. Then when we update info within the Blogroll, that instantly seems online too. Both website and Wordpress are on a single server. Would there be considered a specific Blogroll wordpress plugin that will do that, or perhaps is it generally possible with plug ins?

WordPress plug ins possess a specific structure, and therefore are likely not so functional elsewhere, however as they are on a single server it is simple to query the database having a mySQL query:

SELECT * FROM `wp_links` WHERE `link_visible` = 'Y'

Presuming you are using PHP you can then echo it such as this:

$sql = "SELECT * FROM `wp_links` WHERE `link_visible` = 'Y'";
$result = mysql_query($sql);
echo '<ul>';
while($link = mysql_fetch_array($result)){
    echo '<li><a href="' . $link['link_url'] . '">' . $link['link_name'] . '</a>';
}
echo '</ul>';