If we want to search by name or sku, we can just alter the their respective attribute settings in admin panel. But how to search by mentioning product id?
I thought changing
Mage_Adminhtml_Model_Search_Catalog would does the same but I figured it out that it doesn't.
$collection = Mage::helper('catalogsearch')->getQuery()->getSearchCollection() ->addAttributeToSelect('entity_id') /* added */ ->addAttributeToSelect('name') ->addAttributeToSelect('description') ->addSearchFilter($this->getQuery()) ->setCurPage($this->getStart()) ->setPageSize($this->getLimit()) ->load();