Yes, of course. But a key for a pack that includes DLC can be activated on an account that already owns the base game. As such, a pack key can be used by someone who already owns the base game to get the DLC.
A giveaway creator may not want a pack to go to someone who already owns the primary part of the set, or they might not care either way. Since opinions vary, it's common practice for someone in my position to ask beforehand. :)