If it had inspired or directed the development of the legend, then certainly the Ring would have been seized and used against Sauron; he would not have been annihilated but enslaved, and Barad-dur would not have been destroyed but occupied.
There are no more uses of "annihilate" in the book.
Show samples from other sources
The terrorist wants to annihilate a major American city.
Whenever antimatter and matter collide, they annihilate each other.