Tolkien has said that Middle-earth was meant to represent Europe, with the Shire representing England.
When Frodo sails due West to Valinor, is he actually coming to America?
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In c.1959, Tolkien wrote a text which he titled "The Númenórean Catastrophe & End of “Physical” Aman". In this he explored the idea of Valinor being removed to a spiritual realm and the landmass remaining behind, empty of its inhabitants and becoming America. This text was first published in 2014, as part of "Fragments on Elvish Reincarnation".
Is Aman “removed” or destroyed at the Catastrophe?
It was physical. Therefore it could not be removed, without remaining visible as part of Arda or as a new satellite! It must either remain as a landmass bereft of its former inhabitants or be destroyed.
I think now that it is best that it should remain a physical landmass (America!). But as Manwë had already said to the Númenóreans: “It is not the land that is hallowed (and free of death), but it is hallowed by the dwellers there” – the Valar.
It would just become an ordinary land, an addition to Middle-earth, the European-African-Asiatic contiguous landmass. The flora and fauna (even if different in some [?items] from those of Middle-earth) would become ordinary beasts and plants with usual conditions of mortality.
La Feuille de la Compagnie #3 - Fragments on Elvish Reincarnation
When this was republished in The Nature of Middle-earth, editor Carl Hostetter noted in his commentary that this text was just Tolkien "thinking on paper", and that it doesn't fit with the events of the books, namely Frodo's journey.
It is evident from the haste of his writing and the fluidity of his conceptions that Tolkien is here thinking on paper (as he often did). Not only does some of this thinking apparently contradict long-standing “facts” of the then-unpublished mythology ... but also the númenórean catastrophe events depicted in the already-published Lord of the Rings: e.g., Frodo’s bodily journey to a seemingly very physical Tol Eressëa.
The Nature of Middle-earth - "The Númenórean Catastrophe & End of “Physical” Aman"
There is nowhere else where Tolkien discusses this idea.
In the context of the Akallabêth in the published Silmarillion, no.
Tolkien's original concept of Arda was as a flat world. He later began a project with C.S Lewis where Tolkien would write a "time travel" story and Lewis would write a "space travel" story, but Tolkien couldn't help but write it in the context of his Silmarillion mythology. He abandoned the "time travel" aspect, and the part of the story occurring in the past became Akallabêth, or the Downfall of Númenor.
In short, when Númenor's king Ar-Pharazôn invades the Undying Lands, the Valar call upon Ilúvatar (essentially God) for help. Ilúvatar reshapes the world, drowning Númenor in the process.
The published Silmarillion contains an afterword to Akallabêth (it is double-indented in my copy) in which the following appears:
For even after the ruin the hearts of the Dúnedain were still set westwards; and though they knew indeed that the world was changed, they said: "Avallónë is vanished from the Earth and the Land of Aman is taken away, and in the world of this present Darkness they cannot be found. Yet once they were, and therefore they still are in true being and in the whole shape of the world as at first it was devised".
The Dúnedain of Middle-earth later sent out ships searching for a legendary island, the tip of the highest mountain on Númenor:
Thus it was that great mariners among them would still search the empty seas, hoping to come upon the Isle of Meneltarma, and there to see a vision of things that were. But they found it not. And those that sailed far came only to the new lands and found them like to the old lands, and subject to death. And those that sailed furthest set but a girdle about the Earth and returned weary at last to the place of their beginning and they said: "All roads are now bent."
In other words, the flat Earth was made round by Ilúvatar's intervention.
...and yet the Eldar were permitted still to depart and to come to the Ancient West and to Avallónë if they would therefore the loremasters of the men said that a Straight Road must still be, for those that were permitted to find it.
The Undying Lands were in a sort of superposition of being both in the world and also not in it. If we allow ourselves to extend Tolkien's mapping of Middle-earth as "Europe" on to our round Earth, America would have to be part of the "new lands" that you could get to on the "bent roads" of the now-round Earth.
This was the state of the story when JRRT wrote The Lord of the Rings. When Frodo's ship sailed West to the Undying Lands, it took the Straight Road, so it didn't go to any of the "new lands", including America.
J.R.R. Tolkien played with many ideas throughout his life, some of which contradicted other ideas in their details.
@Ibid has documented some of JRRT's later musings on this subject, and it's interesting to think about what might have been, but these ideas weren't well-developed enough for Christopher Tolkien to include in the final published work.