Display zone code 3 letters intead of name

-- HikaShop version -- : 2.5.0
-- Joomla version -- : 3.4.1
-- PHP version -- : 5.3.24

I would like to be able to display the code 3 letters for a zone in the address country and state dropdowns on the registration page and in the address_template view. Example would be instead of United States of America display USA and instead of Alabama display AL. Is this possible?

For the address_template view, yes, that's possible.
You can use such code:
<?php
$address = $this->params->get('address');
echo $address->address_country_code_3; ?>

For the dropdowns, you can do it with a view override. You would have to hack directly in the administrator/components/com_hikashop/classes/field.php file but I don't recommend it as you'll loose the changes at each update.