Theres a 90% chance she isn't dying, impaled or not impaled.
Obito will either take the hit for her and not sure what will happen after that. Hopefully she would destroy the eye but then itd be Madara vs Sakura (not good for her)
Obito takes hit for her and takes it in the face to destroy rinnegan (still puts it Sakura vs Madara..hopefully it is just half of him)
Obito and her get outta the way and Sakura destroys rinnegan.
Obito kamui's Sakura into the other world safely or injured.
Sakura takes rod to a vital point, and we believe shes dead for a while and its BZ and Madara vs Obito
Sakura gets hit and its not life threatening, and still manages to destroy rinnegan because madara is cut in half.
Sakura gets saved by Sasuke, i sensed possible foreshadowing this chapter that Sasuke will redeem himself somewhat and help her. He would probably save her and Obito and then she would destroy Obito's eye while Sasuke fights half of Madara or Whole Madara.
Sakura surprises us all and somehow dodges the rod, and starts fighting Madara while Obito destroys the eye (Which isnt likely i feel)
Anyways these are the possibilities we seem to be looking at. Sakura is a med nin, top med nin at that....if she was to get sent over to the other dimension fast enough, between her, Naruto's healing thing, or someone like Karin or even Kabuto i don't see her dying.