There's absolutely nothing in Tolkien to support this interpretation that I'm aware of; rather the exact opposite: Frodo did sail West at the end of LotR. There are many passages in Letters that make this clear, for example the following from Letter 154:
But in this story it is supposed that there may be certain rare exceptions or accommodations (legitimately supposed? there always seem to be exceptions); and so certain 'mortals', who have played some great part in Elvish affairs, may pass with the Elves to Elvenhome. Thus Frodo (by the express gift of Arwen) and Bilbo, and eventually Sam (as adumbrated by Frodo); and as a unique exception Gimli the Dwarf, as friend of Legolas and 'servant' of Galadriel.
What Tolkien is also quite clear about is that Frodo did die at some point after his sailing. The purpose of him going West was to obtain healing (both physical and spiritual) from his wounds and ordeal, and to eventually be able to die in a state of "unfallen grace".
There is plenty in the story of LotR that leads to this moment, for example Galadriel's song in Lórien:
Farewell! Maybe thou shalt find Valimar. Maybe even thou shalt find it. Farewell!
And Arwen's words to him in Gondor:
A gift I will give you. For I am the daughter of Elrond. I shall not go with him now when he departs to the Havens; for mine is the choice of Lúthien, and as she so have I chosen, both the sweet and the bitter. But in my stead you shall go, Ring-bearer, when the time comes, and if you then desire it. If your hurts grieve you still and the memory of your burden is heavy, then you may pass into the West, until all your wounds and weariness are healed.
Tolkien, as a general rule, doesn't do metaphor, symbolism or allegory, so you shouldn't really go looking for such alternative interpretations except in cases where they explicitly do exist. In this case everything builds up to Frodo actually sailing West, so we have no cause to assume otherwise.