I don’t think so. In point of “real world referent,” Tom Bombadil was the name given to a(n adult) doll belonging to one of the Tolkien children, I think Priscilla but am unsure. (This is mentioned in passing in either the Letters or Carpenter.)
In terms of who and what he is, remember that Tolkien was a scholar of English literature, with, like Lewis, a taste for the medieval. Bombadil is a character constructed on the lines of the jovial, gamboling nature spirit that is so common an allusion in everything from the Green Knight to the Faerie Queen. Tolkien was enamored of this sort of character; Thingol Greycloak was first drawn as just such a figure. While most of his leading elves are drawn as Our Hero Nobly and Philosophically Faces His Fate, there’s always a hint of the other sense of Elves Engaged in Revelry going on in the background in the elven elements. (And yes, Bombadil is not an Elf in the Studies in Middle-Earth Anthropology sense; what I’m saying is that literarily Bombadil and the Elves are draughts drawn from the same hogshead.
Bombadil is the genius loci, the resident demigod of the particular spot where he is found. And he has the function of taking the four hobbits the first step from the everyday experience of the Shire into a world full of new and strange experiences.
Tolkien was fairly realistic about his own motivations; he is on record as considering himself “a hobbit” in the sense that he depicted them as liking what he liked by way of relaxation. Insofar as he idealized himself and his wife to write them into his story, it’s quite literally graven in stone who they saw each other as: the epitaphs on their tombstones are each one word long: Luthien and Beren. And of course the characters Aragorn and Arwen are depicted as seeing themselves re-enacting the Lay of Leithian knowingly in their own time – which means that inevitably Aragorn takes on a bit of Gary-Stu “if I were a fantasy hero” coloration, though Tolkien was too good a craftsman to allow much of this.
But I believe that has more than a little to do with the decidedly odd motivations of Aragorn-in-the-book, who in some ways seems to be a two-dimensional Missing Prince Reared in Humble Circumstances Who Is Fated to Get the Fabled Princess and Reclaim His Throne character (though again Tolkien is far more subtle than that, but I feel the initial romantic conception interferes with his ability to draw Aragorn as realistic character). The Jackson/Mortensen Aragorn, though still all that, actually has human traits beyond the ability to rise nobly to a challenge: he actually has some self-doubt to conquer, and has to screw up the courage to lay it all on the line for great reward. And Viggo’s Aragorn, unlike the one in the book, can actually feel a twinge of temptation for Eowyn, despite being in love with and pledged to Arwen.
Bombadil, however, is part of a long-standing but extremely moribund literary tradition: slightly more than a personification of the Warwickshire countryside that Tolkien knew and loved, he is both incarnator and protector of that mise en scene. And characters of his ilk, figures out of faerie tied to a particular place, date back to the days of the Greeks (Alpheus and Arethusa, for example, or Narcissus or Hyacinthus) and were relatively common in the more fantastic elements of medieval story.