Did Sauron have the power to bring Melkor back from the Timeless Void? Did he have the power but not the intention, or was it simply impossible?
As far as I know, Sauron suffered the same fate as Melkor, but he came back from his death, which is referred to as "The Void" by Galadriel. In this quote, Galadriel says, "Go back to the Void from whence you came!" So is it possible for a being to come back from the Void?
In the context of your question, Galadriel is implying that Sauron return to the "nothingness" that exists outside Eä (the Universe), which is where he, a follower of Morgoth and abhorrently evil in his own right, belongs.
Among those of his servants that have names the greatest was that spirit whom the Eldar called Sauron, or Gorthaur the Cruel. In his beginning he was of the Maiar of Aule, and he remained mighty in the lore of that people. In all the deeds of Melkor the Morgoth upon Arda, in his vast works and in the deceits of his cunning, Sauron had a part, and was only less evil than his master in that for long he served another and not himself. But in after years he rose like a shadow of Morgoth and a ghost of his malice, and walked behind him on the same ruinous path down into the Void.
The Silmarillion, Valaquenta, Of the Enemies
Note that the "Void" referred to at the beginning of The Silmarillion and after Iluvatar created Eä is different. After Eä was created whatever lay outside of it is now the Void. Thus it is not incorrect to say that Sauron had never been to the Void. He was present in the Void before Eä was created, not referring to the Void which is now the outside of said Universe.
So when Morgoth was cast by the Valar through the Door of Night, beyond the Walls of the World, into the Timeless Void, he is outside Eä, the universe. After the destruction of his Ring Sauron is now in a immensely diminished form - a mere spirit* - and it's unlikely and even more improbable that he'd be up to the task of resurrecting his master. However even if Sauron was alive, it'd still impossible for him to bring Melkor back. Why? Because...
Manwë put forth Morgoth and shut him beyond the World in the Void that is without; and he cannot himself return again into the World, present and visible, while the Lords of the West are still enthroned.
And Sauron, a Maiar, definitely did not have the ability to challenge the Valar themselves. Much less Manwë.
And so Melkor remains in the void until the Dagor Dagorath.
NO
He neither had the power or will to do so.
The Barrier to the Void was sealed by the Valar , and let's not forget that Sauron is a Maia ( junior to the Valar ). This suggests that he did not have the power. Perhaps it might have been possible with the One Ring, but I seriously doubt this ( as the Ring contains Sauron's Maia power, which is still inferior to the power of the Valar who sealed the barrier ).
He did not have the will to do so : if Morgoth was back , Sauron would go back to being his Lieutenant. In Sauron's perspective, this isn't a good idea. Melkor might even snatch the Ring from Sauron ...
PS : It is said that Morgoth will break through the barrier and wage a final war against the Valar - ( a reincarnated ) Turin will kill Melkor and the world will end.
