I doubt it. I am setting myself up for disapointment because I hope they sweep, but I predict that FoTR will not get the awards we would like to see it get. There are logical reasons why they should not let FoTR sweep this time. They can't. They have two more years after this one for movies that have all the promise of being just as high in quality as this one. They are not going to let LoTR and a small film company dominate all the major awards for three whole years and they have to worry about precedent.
Prediction: (write this down)
McKellan wins, and maybe three other more minor awards like song or technical awards. Against all hope, I don't think they will get Director or Picture, although a higher chance for director than picture.
In the next two years, we will see Actor or Supporting Actor nominations for both Elijah Wood and Viggo Mortenson.
I bet they award the whole effort most heavily in the third year.
I read a short "interview" with PJ and Fran on imladris.net, and it made me feel a lot better about the whole Oscars business. Like many of you, I don't expect LotR to take the major awards except for supporting actor, though I do expect technical awards. But in reading the interview, they were saying that while they were hoping for enough box office success to continue with the other movies, they were completely surprised by the critical praise the movie received. Much as I would love to see them take the top honors, and much as I believe they all deserve it for the quality of every aspect of the movie (especially the performances), I won't be devastated if they don't. I think they're all just thrilled and surprised to have received the nominations.
Now...if neither Viggo nor Elijah get nominated for at least one of the upcoming movies, I will be very upset. That's assuming they didn't suddenly lose all of their talent and focus between filming the first movie and filming the other two. ;)