Is it possible to get the currently logged in admin’s IP?

This functionality is not directly available, you’ll have to track the logins inside the database(probably as a transient) & check if that transient is available.

function check_for_admin() {
    $user = wp_get_current_user();
    if(in_array('administrator', $user->roles))
        set_transient('admin_ip', get_ip(), 60*10);
}
add_action('init', 'check_for_admin');

After that you can use get_transient('admin_ip') & check if it’s available

For retrieving the IP, you may use toscho’s code.

EDIT:

The 60*10 in the code means if no admin has been active for last 10 minutes, consider them all offline & cleanup the database.

It’s also possible to delete the transient when user manually logs out, you need to hook into the 'clear_auth_cookie' action to clean up the database.

function clear_the_transient() {
    $user = wp_get_current_user();
    if(in_array('administrator', $user->roles))
        delete_transient('admin_ip')
}
add_action('clear_auth_cookie', 'clear_the_transient');

This code will work in your case when there is only 1 administrator. But this code has a major problem, it deletes the IP from the database even if there are 2 administrators online & only one of them logged out. To overcome that situation, you will have to store the user id as well as their corresponding last activity time in the database.