"Would Ballos have died in the second ending?"
Yes, technically. Ballos would probably have died the moment he was freed... if he hasn't died already long, long ago.
I assume the wild magic was siphoned off by the Core or maybe the chamber just prevented it from escaping... (well too much). If the seal chamber breaks, then the Wild Magic would probably cloud whatever sanity is left in Ballos.
I mean how sane could Ballos be? Depending on your theory of how long he has been sealed away. Being stuck in a room of dead bodies, probably devoid of company; probably doesn't need to eat, sleep, drink...
He'd probably lose almost any trace of humanity he had left! (Though when Quote showed up, maybe it finally allowed him to show a trace of what he was? Still he attacks hardcore, even if he wanted to die.)
Unless, maybe Ballos has been asleep all this time, in his throne? Maybe dreaming about the island. (Was that eye door, Ballos' sleeping power? Watching the hero?)
And after the Core stopped absorbing his power, he was forced awake to his insanity, and soon after transformed into that giant rock with a face...
Maybe Ballos would end up as a super red mist, able to possess anything and cause major havoc, while corrupting the land and the people he passes by... Probably unstoppable...
But, since he was in the undamaged Seal Prison when he went Red Mist, he probably was contained by the prison and eliminated at long last? Or he possessed the prison and it imploded or something crazy... (Or the dead of his kingdom dragged him to his end... After all, Jenka deals with the dead... I think)
Anyway, I think Ballos would have died; but the Wild Magic would become The Red. A mist that turns people into monsters.
... I, however, think that he'd be fine. So many other inhabitants of the island were fine.
Maybe the impact of the island's fall wouldn't damage the interior and top of the island much. After all, the island floated down slowly... maybe suggesting, my theory that those little Cores would have supported the island if Ballos hadn't been forcing it to fall.
But, Ballos' seal chamber looked like it was near the bottom or edge of the island, since you could actually see the outside, in the ghost dog passageway to the seal chamber. Perhaps, the island could have hit precisely in that area during the impact; scraping against those mountains you see in the background during the island's falling scene.
Maybe for those who believe Jenka responsible for stopping the island's fall; could argue that Ballos was pressing down on that one particular point, dragging the island down. And Jenka did all she could to minimize the damage to the rest of the island, and its inhabitants.
Bunches of possibilities...