Very interesting question.
On a basic level of
Tolkien and the message conveyed in his many works, I would say that yes,
Middle-Earth would survive. It is clear that
J.R.R. Tolkien had a strong affinity for showing that good conquers
evil, time after time. Thus, it would be very in character for him to have Middle-Earth still survive and maybe even thrive, with certain evils.
However, on closer speculation, story significance aside, I think this is a question that has to be approached with a lot more care. We know that the
Valar were powerful beings, given the power that they had by Ilu
vatar. In fact,
The term "Valar" is the meaning of "(angelic) powers" in Quenya Elvish.
However, as much as the Valar were the Powers of
Arda, and a force for good, we also know that they
can make bad choices. They can make mistakes with the free will that they have, and in fact they do. The most powerful example of this, of course, found in
Melkor.
Then Ilúvatar spoke, and he said: ‘Mighty are the Ainur, and mightiest among them is Melkor; but that he may know, and all the Ainur, that I am Ilúvatar, those things that ye have sung, I will show them forth, that ye may see what ye have done. And thou, Melkor, shalt see that no theme may be played that hath not its uttermost source in me, nor can any alter the music in my despite. For he that attempteth this shall prove but mine instrument in the devising of things more wonderful, which he himself hath not imagined.’ - AINULINDALË
Here it mentions specifically that
"and mightiest among them is Melkor;" This states that Melkor was the mightiest of the Ainur, thereby above Manwe, and not below him. However, there is still room for doubt here, because Melkor is proclaimed as 'mightiest' which could refer to his power within a particular element. Except for this part, just a few lines earlier:
"To Melkor among the Ainur had been given the greatest gifts of power and knowledge, and he had a share in all the gifts of his brethren."
This tells us that Melkor was not only the mightiest, but had the greatest gifts, and had a share in all others' gifts. In this way, Melkor surely must have been the highest.
So after all of this, it seems only plausible to believe that the world of Middle-Earth would have indeed survived, even with two Valar gone. After all, it was the greatest of them all that fell to darkness, and it simply seems like it could not get worse. I believe that if a minor
Vala fell to darkness, there would be little effect that would change the survival of all Middle-Earth.
However, if it was a greater Vala, like Manwe or
Varda, I could see it possibly making a long-term effect. After all, while the Valar did prevail against
Morgoth, they struggled. And he was just one Vala. So if there were more of the Valar, perhaps two of the greatest, that had fallen to evil, the outcome could have been different. If evil had prevailed against the good of the Valar, then I suppose it is possible that Middle-Earth would not have survived, leastward, how it did.
IN SUMMARY:
To me, I believe, it would depend on which two Valar fell to darkness, and whether they were fully corrupted, or only partially.