It is possible thru rewrite or observer: (observer is better to prevent rewrite conflicts)

### Using Observer ###

Configure your 2 observers: loading the column to grid and loading of collection

    <adminhtml>
        <events>
            <core_block_abstract_to_html_before>
                <observers>
                    <{observer_name}>
                        <class>{namespace}_{module}/observer</class>
                        <method>beforeBlockToHtml</method>
                    </{observer_name}>
                </observers>
            </core_block_abstract_to_html_before>
            <eav_collection_abstract_load_before>
                <observers>
                    <{observer_name}>
                        <class>{namespace}_{module}/observer</class>
                        <method>beforeCollectionLoad</method>
                    </{observer_name}>
                </observers>
            </eav_collection_abstract_load_before>
        </events>
    </adminhtml>

Then create your observer class with the methods in the declaration 

    class {Namespace}_{Module}_Model_Observer
    {
        public function beforeBlockToHtml(Varien_Event_Observer $observer)
        {
            $grid = $observer->getBlock();

            /**
             * Mage_Adminhtml_Block_Customer_Grid
             */
            if ($grid instanceof Mage_Adminhtml_Block_Customer_Grid) {
                $grid->addColumnAfter(
                    '{column_code}',
                    array(
                        'header' => Mage::helper('{Module}_customer')->__('{{column_name}}'),
                        'index'  => '{column_code}'
                    ),
                    'entity_id'
                );
            }
        }

        public function beforeCollectionLoad(Varien_Event_Observer $observer)
        {
            $collection = $observer->getCollection();
            if (!isset($collection)) {
                return;
            }

            /**
             * Mage_Customer_Model_Resource_Customer_Collection
             */
            if ($collection instanceof Mage_Customer_Model_Resource_Customer_Collection) {
                /* @var $collection Mage_Customer_Model_Resource_Customer_Collection */
                $collection->addAttributeToSelect('{attribute_code}');
            }
        }
    }

See this answer: https://magento.stackexchange.com/a/5986/21518

### Using Rewrite ###

Rewrite the grid block's `_prepareCollection` method and add your column to the collection.

See this answer: https://magento.stackexchange.com/a/5975/21518