No - Tolkien's Time Travel book never got past the first few Chapters. It's called
The Lost Road and Christopher Tolkien published what we have of it in
The Lost Road and Other Writings as part of the
History of Middle Earth. Bear with me - this is horribly complicated but really interesting! (At least to me

).
He creates his 'time-travel' through the means of reincarnation (which is, in itself, fairly amazing given his beliefs). Briefly and from memory (it really is very complicated) Albion (a philologist like Tolkien) keeps having strange dreams, visions and flashes of a lost language and people. Eventually it reaches a crisis where he is told by a vision of Elendil that he can have his great desire: to step back into the past, but only if his son goes with him. He and his son (who also has dreams) choose to go back and after falling into a stupor he wakes
AS Elendil himself and his son is Elendil's son. As this is very early in his writing, at this time Elendil only has one.
In the next chapter we are with Elendil (Albion) who is also having strange feelings that he is seeing his life through someone else's eyes. Everything he looks at seems new, as though he is seeing it for the first time. He is a very troubled man - Sauron is leading the King and all Numenor astray and Elendil intends to stop him. He is, in fact, a secret rebel who sees Sauron as evil. His young son, though, admires Sauron and is a keen follower of him. He likes the changes he makes, the new temple and the new songs that the young people are now singing. Elendil, believing he can bring his son around, tells him what he really believes Sauron to be and what must be done.
Tolkien never wrote any more, but his intention was for the son, Herendil, to ultimately betray his father to the king.
There were also to be other chapters featuring other incarnations of the Elendil/Albion figure. One was to be Aelfwine, living in Anglo-Saxon England, and also a possible Lombard story. All these would tie Elendil, through time and many descendents, to Albion in a direct line and also tie Numenor through to Tolkien's beloved England. I think, in the end, the idea was just too complex and too hard to fit into the rest of his mythology which was just on the verge of completely changing direction - abandoning forever his early idea that Tol-Eressea (the Isle of the elves) was actually now England. Aelfwine (originally called Eriol the Mariner) was always a figure in Tolkien's earliest writings who would receive all the history of the elves from them (after finding their land at the end of a voyage) and bringing their stories back to men. He was the original Elf Friend (that is what his name actually means) like Elendil, Tuor, Bilbo and Frodo. Aelfwine was a known Anglo-saxon name, found in many other varients across Europe at the time, and the meaning fascinated him. But I think things got a lot easier (story wise) for Tolkien when he abandoned him!
All this complexity is actually a vastly simplified summary of all the ins and outs of this story

.
The Lost Road and Other Writings also contains fragments of another story:
The Fall of Numenor in two versions. This is also part of his whole time-travel thing and was to have formed the end of the book:
We (Lewis and Tolkien) agreed that he should try 'space-travel' and I should try 'time-travel'. His result is well known. My effort, after a few promising chapters, ran dry: it was too long a way round to what I really wanted to make, a new version of the Atlantis legend. The final scene survives as The Downfall of Numenor.
The whole thing is a hard to pin down as the great waves tossing Numenor into the depths

.