Theoretically enough, I don't think Katsuyu can actually die. Out of the three summons, Katsuyu is more less a utility aid corresponding with the Byakugou. A helpful medic pack of sorts, but since this battle doesn't directly summon Katsuyu via Tsunade — her healing abilities would be restricted. However, that's irrelevant; Katsuyu's true size is unknown. Tsunade stated that with both her own and Sakura's Byakugou activated was only enough to summon 1/10 of Katsuyu. Tsunade alone was able to summon one portion of Katsuyu which was relatively the same size as Saiken. Saiken looses, fact is Katsuyu would be the same comparison as if a human would stand next to a tailed beast. Saiken being the human; Katsuyu the tailed beast. Either Katsuyu produces an avalanche of corrosive acid or simply rolls over and squashes Saiken; Saiken dies.