Yes you can add this to an existing attribute set, normally set as "default" within Magento. When you add an attribute you can assign a default option if most of the time these are the same setting, then when adding new products it will default to this option.
If you need to update existing products on mass you can update attributes in bulk if you go to: Catalog > Manage Products > Tick the products you want to edit with the same attribute option > From the actions dropdown select "update attributes" >
NOTE: You will now be editing all products you previously highlighted so be careful,
find the attribute you want to edit > click the "change" check box > update the attribute.
This should allow you to add and change your new attribute across multiple products far quicker, hope this helps.