Or would he have done it even better? Would Auir have even been lost or Amon taken him over?
Aiur would have fallen to amon either way. Because outside of those who cut their nerve cords Amon controlled all zerg and protoss forces on the planet. Aratnis after being freed did not have much of an army to continue the fight.
As for Amon taking over Tassadar, we have no reason to believe he couldn’t have done it as long as Tassadar was connected with the Khala.
Though Tassadar had experimented with using Dark Templar energy, so maybe he could have resisted, just like how Tal’darim are not controlled by Amon despite having their nerve cords (well, he just uses other means, but getting to Tassadar would be trickier)
The Tal’darim aren’t connected by the Khala. Tassadar as a templar is connected with it and void energies or not Amon has straight access to his head.
If Tassadar lives, he has Artanis to help him, so yes.
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Tassadar could have sacrificed himself to save everyone. He would have let Artanis do the political agendas and him be on the frontlines leading battles.