if somebody already owns the base game but uses a key for the "Complete Edition" of said game, i do believe that everything that the person doesn't have will be activated on their account - it's just that they won't receive an additional copy of the base game / whatever DLC they did already have; so the question becomes if it'd be worth it to basically waste that copy of the game just for the DLC

the package costs $6.99
base game $4.99
DLC $2.99 * 2

so technically the DLC make up the bulk of the package, but only just barely