The Three on Sauron's hand

[Lord of Angmar]

I think that the Three Elven Rings would probably be useless for any purpose, good or evil, if Sauron had won a victory over Middle Earth. They were made by the Elves and thus would probably either die with the Elves or become useless to any new bearer. Or, just as Morgoth was burned by the Silmarils, perhaps they would have an ill effect on Sauron if he put them on. This theory I doubt very much, however. I think their becoming useless would probably be the most likely occurrence.

Would they accelerate the decay of time, to bring the world to an end, and accelerate Morgoth's return?

I do not think the Elven Rings would have the power to hasten Morgoth's return, nor to end the world.