What is the Chance of the Valar Fighting for the Free People During the Third age?

[Ivriniel]

Had Sauron won the ring back and somehow increased his might, or drew on Saruman's as a subject of Sauron (we know that Saruman was cited as eventually equipped to "make his own Ring") perhaps Sauron could have smitten and broken the Doors of Night, and as such, Melkor returns.

That would or could trigger the Dagor Dagorlad in a variation of it, and so the Valar enter the conflict that way.