How would Sauron fare?

[Lord of Angmar]

Even then [without perfect unity] they would have prevailed... were it not for the treachery of Men.

Gwaihir, that quote means that they would have defeated Morgoth at the Nirnaeth Arnoediad, which is only a battle not the entire war. But they could almost certainly not have defeated Morgoth without the aid from the Valar, as was stated several times in the Sil and other works... I will try to find the quote in the beginning of the Sil, as I believe Mandos or Manwe said it.