Is it possible to kill the early versions of Godcat?

If EBF4 there are two versions of Godcat that appear as a surprise attack. The first ambush occurs right after the Crystal Golem boss, the second is inside the lava zone inside the jungle.

In these battles, Godcat have massive stats and will be almost impossible to hit her. God cat will do massive single target damage that instantly kills characters. After some turns she disappears and summons some more killable foes.

If you were to grind enough before these encounters and get really good equips and skills, would you be able to kill Godcat? And if so, what effect would it have on the game?