But, the overarching God, that Frodo could and did call on in necessity (compare to our OMG! Pathetic!), was there to make Frodo succeed while the evil beings carrying us to Hell have to count on us not calling on that God. The ring drew the black riders, but could not call them, without getting Frodo to put it on. But, Frodo could call on Elbereth.
No intention of nit-picking here but, since Tolkien was indeed Roman Catholic, it might be prudent to point out that Elbereth is more like the Virgin Mary than God. The mother of Jesus is especially revered in Catholicism, especially in Mediterranean and Latin American countries, and many Catholics direct their prayers to her rather than to God the Father. Similarly, Elbereth was not God; she was a Vala, which is sort of equivalent to an archangel. She was in fact the Queen of the Valar (as Mary is often called "Queen of the Angels") and the most beloved of all the Valar by the elves, and they called to her in their songs more than any other Vala. In Middle Earth, God (Eru, a.k.a. Illuvatar) was always more remote, was almost never addressed directly, and never appeared in any form visible to elves or humans.