Andy has the right of it. The Choice did not exist until the problem of Earendil and Elwing arose, and it took a special ruling by Eru.* Before that time - i.e. during Dior's lifetime - the Mandos Rule was in effect: any descendant of a Man was a Man.
And, as mentioned above, Luthien had become human before Dior was born anyway. The same situation** would apply to Eldarion in the Fourth Age.
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*Even then it applied only to them and their descendants, not all half-elves.
**with a couple of technical differences
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The entire plot of The Lord of the Rings could be said to turn on what Sauron didn’t know, and when he didn’t know it.
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