Currently, when adding a Stocktake and searching for a Product using a Product Code the user can only see the Product name not the code. However, when searching in the Search for anything the User can see the Product Code. Replenishment behaves in the same way as Stocktake and the Stock Movement Report behaves in the same way as the Search for anything bar.
As mentioned in Support Dev by Nic, it would be a nice improvement to add the product code to all relevant search results in CartonCloud.