CURRENT SOLUTION
It seems like the initContent() function is NOT being executed when submitting the registration form in Prestashop 1.7.6.3... (perhaps above solutions worked in earlier 1.7.x versions?)
Therefore, I was NOT able to apply the above address save logic within the AuthController.php file...
HOWEVER - instead of adding to AuthController.php --- I'm able to update the ps_address file by updating override/classes/form/CustomerPersister.php
(Clear cache after updating below code)
1) Within CustomerPersister.php -- find the 2nd occurrence of
$ok = $customer->save();
2) Directly below -- Add your Address Saving Code (slight variation of above solutions to allow same code to work within this logical position)..
//address saving
$address = new Address(
null,
$this->context->language->id
);
$address->id_country = (int) Tools::getCountry();
$address->address1 = Tools::getValue('address1');
$address->postcode = Tools::getValue('postcode');
$address->city = Tools::getValue('city');
$address->phone = Tools::getValue('phone');
$address->vat_number = Tools::getValue('vat_number');
$address->firstname = $customer->firstname;
$address->lastname = $customer->lastname;
$address->id_customer = (int) $customer->id;
$address->id_state = 0;
$address->alias = 'My Address';
if($address->save()){
$should_redirect = true;
} else {
$customer->delete();
$this->errors[] = $this->trans('Could not update your information, please check your data.', array(), 'Shop.Notifications.Error');
$this->redirectWithNotifications($this->getCurrentURL());
}