Is it possible allow search only for some countries?

Yes, It's possible with a small customization.

Please add following code in the file functions.php of your theme. In our example we limit search for Australia and New Zeland

add_filter('yith_sl_autocomplete_options', 'yith_sl_autocomplete_set_restrictions');

if (!function_exists('yith_sl_autocomplete_set_restrictions')) {
        function yith_sl_autocomplete_set_restrictions($options)
    {
                $options = array(
                        'componentRestrictions'    =>    array(
                            'country'    =>    ["AU", "NZ"]
            )
        );
        return $options;
    }
}

Feel free replace our example values "AU" and "NZ" with your favourite ones.

You find the complete list of countries ISO codes at following link