Do you have product_id and not item_id right?
If in this case it is not possible to obtain the product identifier without completing all the elements.
Mage_Sales_Model_Quote::getItemByProduct($product);, , .
:
$product = Mage::getModel('catalog/product')->load($pid);
$item = $quote->getItemByProduct($product);
$quote->getCart()->updateItem(array($item->getId()=>array('qty'=>$qty)));
$quote->getCart()->save();
:
$quote->hasProductId($pid) to check if product is in the cart
($qty!=$item->getQty())
, ...
, - , , .
,