I have to make a correction. I think you are absolutely right about the fact that Morgoth did not have a direct connection with Sauron during the 2nd and 3rd Age, but that he left an unremovable imprint on Sauron's being, much as all of Arda.
And about the Dagor Dagorath. I do not remember reading that it is way away into the future. I think they say that it will be on an unknown time, possibly in a far distance, but possibly not, when Melkor returns to this Earth to bring it into its end.
And I do believe that the Valar would come here to rescue the free peoples of M.E. had Sauron succeeded and conquered all. Why? Simply because that's their mission, their task, appointed to them by Eru: to look after our well being on this world. They would not accomplish such a mission if they left us under Sauron's dominion...
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"In place of a Dark Lord you will have a Queen! Not dark but beatiful and terrible as the Dawn! Treacherous as the sea! Stronger than the foundations of the Earth! All shall love me and despair!"
--- Galadriel when tempted by the One Ring.
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