As much as I would like to vote, I can't. I've just spent some time rereading relevant passages in the Letters. Estelyn makes excellent points, however, Tolkien seems ambiguous on the subject. He repeatedly uses the word "God" (capitalized) to refer to Eru (as one example of this ambiguoity.) He also uses the phrase "true God" a number of times.
I think there may be a reason why he did not write about a more involved creator.
Quote:
The Incarnation of God is an infinitely greater thing than anything I would dare to write.
-Letter 181 author's emphasis
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He seems to have been afraid of writing a mischaracterization. I think he wanted the parallel (or maybe "similarity") to be there but didn't want to push it too far.
I think the question is unanswerable.