For the registration, you would have to build a joomla user plugin and check the address post code in your plugin.
For the orders, yes. You can turn on the option "Force shipping regardless of weight" in the config, under the tab checkout. Then, in the menu System->Shipping methods->manual shipping methods plugin, you can create new shipping methods with post code restrictions to allow all post codes except the ones you don't want. That way, during the checkout, if the system doesn't find any shipping method for the address of the user, it won't let him finish the order.