If you remember Sauron didn't know about the 3 elven rings until after he had completed the One ring. It was through the 3 rings that the elves heard the ring spell! His intentions was to rule the elves through the other 18 rings (9 & 7). So his plan failed that way. He wasn't invincible when he wore the ring, he would have lost the battle of the LA with or without the ring because he was killed by Gil-Gilad & Elendil, he was already 'dead' on the floor when Isildur cut the ring off! So without the ring he would almost certaintly lost! The one ring could only rule the 3 rings in the 3rd age, after the Elfs had been using them. So his plan failed first because the elfs took off their rings but he would had sucseeded in the 3rd age if he regained it.
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