I don't know what Tolkien would have thought of the "almost giving in" scene, but it's my favorite of TTT
You're probably right that he wouldn't have liked it just because there's so much sexual tension and all that (something the books are quite devoid of).
However, I think that if Eowyn's despair were to grow great enough, she would have given in. Maybe. Who knows? All I know is it's fun to write about in AU fanfiction!