[Sharkû]

I am afraid textual evidence largely disproves the theory.

Iarhen argues that Sauron's goal in his conquest of Middle-earth could only be "humans and Morgoth", because he would not dare to provoke Valarin intervention for anything else. Herein lies the first weak argument.
Sauron did not assume the Valar would intervene in any case. This was mainly founded on the fact that they did not take direct action in the whole of the Second Age, when Númenor rose against Valinor, and the latter was only removed from the world; and when Sauron's dominion could have been great enough to provoke the Valar already. Cf. Myths Transformed:

<font size ="-2">"He [Sauron] probably deluded himself with the notion that the Valar (including Melkor) having failed, Eru had simply abandoned Eä, or at any rate Arda, and would not concern himself with it any more. It would appear that he interpreted the 'change of the world' at the Downfall of Númenor, when Aman was removed from the physical world, in this sense: Valar (and Elves) were removed from effective control, and Men under God's curse and wrath." (HoME X, 5, MT i).

On the very same ground, he would see absolutely no need to "confront a Valinor host" actively.
Knowledge of Morgoth's ultimate defeat had therefore different meaning for Sauron. We know that Sauron could be greater than Morgoth (cf. Myths Transformed), and I explained above how Sauron viewed the Valar after the Fall of Númenor. Sauron's motives after the fall or Morgoth for staying in Middle-earth were also not as explained. Instead, see below the quote from Letter 153.

Furthermore, why ever should Sauron even want Melkor to return? One could argue that this would aid his position in his weak times, but Iarhen and Gwaihir were assuming Sauron would want him to come back when he was already at a peak of his power. Why should Sauron, as a supreme God-King of Middle-earth, want to subordinate himself again? Nor would he, in such a position of power, want it to end by bringing Ragnarök about!

Sauron was also aware of Eru's "curse and wrath" over Men. It should not be assumed that he had high plans for himself where Men would play a pivotal part, knowing that Eru might be watching.

Gwaihir, on the other hand, goes so far as to have Morgoth present in the 2nd and 3rd Ages.
However, we can diqualify actual, direct influence right away: "Nonetheless the breaking of Thangorodrim and the extrusion of Melkor was the end of 'Morgoth' as such, and for that age (and many ages after)." (HoME X, 5, MT VII iii)
Morgoth met his end like this:

<font size="-2">"He [Morgoth] was judged, and eventually taken out of the Blessed Realm and executed: that is killed like one of the Incarnates. It was then made plain (though it must have been understood beforehand by Manwë and Námo) that, though he had 'disseminated' his power (his evil and possessive and rebellious will) far and wide into the matter of Arda, he had lost direct control of this, and all that 'he', as a surviving remnant of integral being, retained as 'himself' and under control was the terribly shrunken and reduced spirit that inhabited his self-imposed (but now beloved) body. When that body was destroyed he was weak and utterly 'houseless', and for that time at a loss and 'unanchored' as it were. We read that he was then thrust out into the Void." (HoME X, 5, MT VII iii)

With this quote, we can also make the importance of Morgoth dissipated throughout Arda relative. For one, he no longer possessed control over this, and was too remote to do so even if he still were able to control it, since he was in 'the Void', outside Terra in the solar system.

Sauron's establishing a Morgoth cult on Númenor had totally different reasons than Gwaihir argued:

<font size="-2">"But there was seen the effect of Melkor upon Sauron: he spoke of Melkor in Melkor's own terms: as a god, or even as God. This may have been the residue of a state which was in a sense a shadow of good: the ability once in Sauron at least to admire or admit the superiority of a being other than himself. Melkor, and still more Sauron himself afterwards, both profited by this darkened shadow of good and the services of 'worshippers'. But it may be doubted whether even such a shadow of good was still sincerely operative in Sauron by that time. His cunning motive is probably best expressed thus. To wean one of the God-fearing from their allegiance it is best to propound another unseen object of allegiance and another hope of benefits; propound to him a Lord who will sanction what he desires and not forbid it. Sauron, apparently a defeated rival for world-power, now a mere hostage, can hardly propound himself; but as the former servant and disciple of Melkor, the worship of Melkor will raise him from hostage to high priest. But though Sauron's whole true motive was the destruction of the Númenóreans, this was a particular matter of revenge upon Ar-Pharazôn, for humiliation. Sauron (unlike Morgoth) would have been content for the Númenóreans to exist, as his own subjects, and indeed he used a great many of them that he corrupted to his allegiance." (HoME X, 5, MT VII i)

Morgoth's "enduring evil" was only important very indirectly. On the contrary, much of what Sauron was able to work with was his own achievement:

<font size="-2">""Sauron, however, inherited the 'corruption' of Arda, and only spent his (much more limited) power on the Rings; for it was the creatures of earth, in their minds and wills, that he desired to dominate. In this way Sauron was also wiser than Melkor-Morgoth. Sauron was not a beginner of discord; and he probably knew more of the 'Music' than did Melkor, whose mind had always been filled with his own plans and devices, and gave little attention to other things. The time of Melkor's greatest power, therefore, was in the physical beginnings of the World; a vast demiurgic lust for power and the achievement of his own will and designs, on a great scale." (HoME X, 5, MT VII i)

"It is thus probably to Sauron that we may look for a solution of the problem of chronology. Though of immensely smaller native power than his Master, he remained less corrupt, cooler and more capable of calculation. At least in the Elder Days, and before he was bereft of his lord and fell into the folly of imitating him, and endeavouring to become himself supreme Lord of Middle-earth. While Morgoth still stood, Sauron did not seek his own supremacy, but worked and schemed for another, desiring the triumph of Melkor, whom in the beginning he had adored. He thus was often able to achieve things, first conceived by Melkor, which his master did not or could not complete in the furious haste of his malice.
We may assume, then, that the idea of breeding the Orcs came from Melkor, not at first maybe so much for the provision of servants or the infantry of his wars of destruction, as for the defilement of the Children and the blasphemous mockery of the designs of Eru. The details of the accomplishment of this wickedness were, however, left mainly to the subtleties of Sauron." (HoME X, 5, MT X)

Here we are also presented with the definite statement that Sauron was only working on Melkor's designs as long as he was his servant. With the passing of his Master, he had own plans:

<font size="-2">""He [Sauron] was given an opportunity of repentance, when Morgoth was overcome, but could not face the humiliation of recantation, and suing for pardon; and so his temporary turn to good and 'benevolence' ended in a greater relapse, until he became the main representative of Evil of later ages. But at the beginning of the Second Age he was still beautiful to look at, or could still assume a beautiful visible shape – and was not indeed wholly evil, not unless all 'reformers' who want to hurry up with 'reconstruction' and 'reorganization' are wholly evil, even before pride and the lust to exert their will eat them up." (Letter 153)

Thusly, Sauron's and Morgoth's motives in their respective aeras clashed. Sauron seeked dominion, Morgoth annihilation.

As to the question of the Valar intervening in case of Sauron's supremacy in Middle-earth, we may look at Letter 156:

<font size="-2">""The Valar had no real answer to this monstrous rebellion - for the Children of God were not under their ultimate jurisdiction: they were not allowed to destroy them, or coerce them with any 'divine' display of the powers they held over the physical world. They appealed to God; and a catastrophic 'change of plan' occurred." (letter 156).

Sauron's assumption that Men were more likely to be affected by an intervention of Eru than of the Valar is therefore not at all unfounded.