Would it be possible to support two address fields at user registration?

Yes, you would need to create and load a modified version of the addresses.js though (to support all fields). Below is an example; obviously, you'll need to substitute ID/array index information. As far as auto-population, you'd need to create a javascript listener for a 'Same As' checkbox or something to carry over data or disable the fields etc.

example_module.module

function example_module_form_alter(&$form, $form_state, $form_id) {
  switch ($form_id) {
    case 'user_register':
      drupal_add_js(drupal_get_path('module', 'example_module') . '/example_module_addresses.js');
      module_load_include('inc', 'addresses');
      $form['billingcountry']['#options'] = _addresses_country_get();
      $form['billingstate']['#attributes'] = array('style' => 'display: none;');
      $form['shippingcountry']['#options'] = _addresses_country_get();
      $form['shippingstate']['#attributes'] = array('style' => 'display: none;');
    break;
  } // end switch;
} // end function;

example_module_addresses.js

Drupal.behaviors.addresses = function(context) {
  // Bind country changes to reload the province field and
  // load province select element onLoad, do it once.
  // See http://drupal.org/node/817244
  $('#edit-profile-billingcountry',context)
    .addClass('addresses-processed')
    .bind('change',function(){performProvinceAjax(this, '#edit-profile-billingstate');})
    .change();

  $('#edit-profile-shippingcountry',context)
    .addClass('addresses-processed')
    .bind('change',function(){performProvinceAjax(this, '#edit-profile-shippingstate');})
    .change();

  // Make province select list call
  function performProvinceAjax(countryElement, child) {
    // Country field's related province element
    var provinceElement=$(countryElement).parent().siblings().children(child);

    $.ajax({
      type:'GET',
      url:Drupal.settings.basePath,
      success:updateProvinceField,
      dataType:'json',
      data: {
        q:'addresses/province_ajax',
        country:$(countryElement).val(),
        field_id:provinceElement.attr('id'),
        field_name:provinceElement.attr('name'),
        passback:provinceElement.parent().attr('id'),
        //province:provinceElement.val(),
        province:$(child).val()
      }
    });
  }

  // Populate province field
  function updateProvinceField(data) {
    if(data.hide){
      $('#'+data.passback).hide();
    }else{
      $('#'+data.passback).show();
    }
    $('#'+data.passback).html(data.field);
  }
};