Immortality and the sons of Elrond

[Inziladun]

Originally Posted by William Cloud Hicklin

As for Elladan and Elrohir, they certainly remained for a certain time after Elrond sailed; Tolkien wrote (can't find the cite) that after Galadriel left, and Lothlorien started to fade, Celeborn went to Rivendell to live with them, for a while.

That's from Appendix B.

But after the passing of Galadriel in a few years Celeborn...went to Imladris to dwell with the sons of Elrond.

It doesn't say that the choice had been made one way or the other, but isn't it still possible they had chosen, and had decided on mortality?