Interesting point, Sauron The White.
Sauron poured much of his power into the Ring, but even then he was so powerful that his diminished self could still command a very mighty army from his stronghold in Mordor. Had he the Ring again his power would have been greater, though this might not have affected the strength of his army to any important degree -- they would still have won, regardless.
It would have been checkmate for the Elves, though, because of the Ring's dominance over the Elven rings.
So if the Ring is kept from Sauron, then his enemies have more time to conjure up a crazy, game-saving move -- and isn't that just what happened?
If Sauron gets the Ring, all hope is gone and the end will be a lot sooner.