No, she doesn't have the Karlstein.  And she doesn't get Premium outfit boxes because there is no costume slot for her Sol.  Classic outfit boxes contain 6 slot pieces (head, body, boots, gloves, main weapon, subweapon), Premium contain 7 (classic box contents + awakening weapon).

It's more NA, NA wants shai to be killed off, look around. No one wants to play one, no one buys anything for her, no one talks about her, other than the handful of us that love Shai as a game character in a game.