There is no hook. The only place to print something to the screen is at the beginning of the field where $author_url = get_comment_author_url();
is executed.
Sample:
add_action( 'load-edit-comments.php', 'wpse_64737_comment_actions' );
function wpse_64737_comment_actions( $url="" )
{
if ( 'load-edit-comments.php' === current_filter() )
{
add_filter( 'get_comment_author_url', __FUNCTION__ );
return;
}
echo '<p>Output in the Author field!</p>';
return $url;
}
You can move that output with JavaScript to the bottom of the field later.