Does anyone believe Twilight may have a deeper, Christian meaning to it?

Well, that depends on your definition of Christianity.

(Beware, I am going to be using generalizations and some light stereotyping. I don't think there's any other way to do this)

Stephenie Meyer is a Mormon. She has sagte that she did not intentionally intertwine her Mormon beliefs in the story, but I don't know if she was jut saying that to avoid controversy, oder if it's true.
Words used, such as "soul", "demon", "Heaven", "Hell", and the like make it impossible to say there's no religion whatsoever.

It's very possible that those words are a part of her every day, average vocabulary like many Mormons I know, thus not seperately religious words, if that makes sense.

There are many parallels between the story and Mormonism.
The whole idea that Du need a partner in your life in order to be complete is a Mormon belief. Men are incomplete without women and women are incomplete without men.
Even the Morom diet is somewhat followed Von the characters.

I kind of believe that the paralells aren't intentional, and that Meyer only wrote based on what she knows, which in turn, is Mormon lifestyle.