My answer:
Of course fantasy can point to Christ, there is nothing inherently diabolical about that particular genre.Lord of the Rings was not intended to be a distinctly Christian allegory like The Chronicles of Narnia. Although Lewis and Tolkien were friends, I have heard that Lewis' friendship with Tolkien was instrumental to his conversion to Christianity, I think they had two different motivations for writing the things they did.
Lewis' stories were written in, what seems to me, an Apologetical manner. He attempted to present the Gospel in a manner that would reach all sorts of different people. Reading Narnia you can't help but see Christ and the Gospel.
Tolkien, on the other hand, wrote with the great themes of Christianity in mind i.e. life, death, good, evil, friendship, love, hate. He may not have had storylines and characters that could be directly traced to the Bible, but they were there indirectly.
Just reading The Lord of the Rings and The Hobbit will not give you a sense of the big picture that Tolkien has placed his characters in. To get that you need to read The Silmarillion. In that work you are told of the greater forces that are at work in LoTR. You have the one Creator God, his two classes of servants: the Valar, and the Maiar, the story of how the greatest of his servants desired to serve himself and rebelled against the Creator God, the creation of the world, the creation of Elves and Men. It is really quite fascinating. I could detect threads of thought in The Silmarillion that were distinctly patterned after what we, as Christians, believe.
I hope that helps. If you want, come ask your Tolkien questions over on The Hobbit Hole. There are people there that are much more knowledgeable about Tolkien than myself. ;^)
I just wanted to share this with you all so that I could get your feedback to see if I was way off base with my answer.