Well, you can certainly read the story in that way if you choose to. Tolkien left the reader free to interpret as it pleases. As he said in the preface to the second edition:
The Lord of the Rings has been read by man people since it finally appeared in print; and I should like to say something here with reference to the many opinions or guesses that I have received or have read concerning the motives and meaning of the tale. The prime motive was the desire of a tale-teller to try his hand at a really long story that would hold the attention of readers, amuse them, delight them, and at times maybe excite them or deeply move them...As for any inner meaning or 'message', it has in the intention of the author none. It is neither allegorical nor topical. As the story grew it put down roots and threw out unexpected branches...I cordially dislike allegory in all its manifestations, and always have done so since I grew old and wary enough to detect its presence. I much prefer history, true or feigned, with its varied applicability to the thought and experience of readers. I think that many confuse 'applicability' with allegory'; but the one resides in the freedom of the reader, and the other in the purposed domination of the author.
An author cannot of course remain wholly unaffected by his experience, but the ways in which a story-germ uses the soil of experience are extremely complex, and attempts to define the process are at best guesses from evidence that is inadequate and ambiguous. It is also false, though naturally attractive, when the lives of an author and critic have overlapped, to suppose that the movements of thought or events of times common to both were necessarily the most powerful influences.I put the sections I thought relevant in bold. Tolkien left the reader and critic free to interpret the tale as they please. However, if the tale is mystical for you, then the mystical is unknowable and incomprehensible by definition. What we do know is the wonderful story Tolkien wrote. He created a great work of the imagination.
Actually as i stated many of the academics in Tolkien—A Celebration read the book that way. Indeed, that reading is not inconsistent at all with what they have to say about the subject. The book could not have been written in the way it was without that Tolkien’s Catholic perspective. But thank you for your license to read it as others have :) Oh -—see eg Sean McGrath, The Passion According to Tolkien.