If Sauron prevailed...

[Inziladun]

Originally Posted by Zigûr

Ring or no Ring, Sauron's will and attention was not omniscient or omnipresent, and Cirith Ungol alone shows how easily his own servants could fall to fighting each other. This was especially a problem with Orcs, as Professor Tolkien observes in the essay 'Orcs' published in Morgoth's Ring.

Then again, as Frodo, who, through possession of the Ring had special insight into Sauron's will and his rule over his servants noted to Sam, the two Orcs hunting them after their escape would have forgotten all about whatever quarrel they had if they'd spotted the Hobbits.
So maybe, as long as Sauron gave his subjects an external enemy to vent their anger and lust for conflict toward, his realm could have endured. Perhaps the utter subjugation of the West, once accomplished, would have indeed led to an insane plan to conquer even Valinor, and take down the 'false gods' of the West. I can see Sauron eventually getting arrogant enough to try it, or at least to feign that was an ultimate goal of his.

For a 1984 parallel, the "war' against the West need not even be actual. Sauron could manufacture 'attacks' by the remaining Elves and Men and blame the Valar, turning whatever hate and frustration fumed in Mordor's minions always away from himself.