If the global of the script page function utilizes $userob on that page you can:
Detect a Guest:
if(!$userob->is_logged_in) {
echo("Guest");
}
Detect a Logged in User:
if($userob->is_logged_in) {
echo("HAI!");
}
You could use those bits to set a variable and have a template trigger read the variable and display an island.
If you mean in the sidebars, you'd have to rejigger how they function in order to inject an additional island only for regged users.