Conclusion
I think a strong case can be made for the demon theory. There is definitely some good evidence to suggest that M. Night had a few tricks up his sleeve with this script and there's a hidden narrative within the main story. The detracting evidence, however, is strong I think. While less voluminous than the supporting evidence, it nonetheless punches some pretty big logical holes into the demonic interpretation. (Although one could argue that demons are masters of deception.)
One thing that is definitely true is that the demon theory allows you to resolve certain narrative problems like, "Why would the demons come down without protective suits on?" and "Really? WATER?!"
Personally, I think that one's own openness to the theory will depend on how much weight you place on certain factors. If you just can't get over the detracting evidence, then that's understandable. On the other hand, if you find the supporting evidence to be strong enough that you clearly feel like Shyamalan is trying to say SOMETHING that's not obvious on the surface, then I can definitely understand that as well.
For me, I think the movie works (albeit imperfectly) as a film about an alien invasion. I also think it works (albeit imperfectly) as a movie about demonic forces at work. And I know that I'll never be able to watch it again without interpreting it on both levels, regardless of what the director intended. Though I will say this: If the theory is correct, and M. Night intentionally encoded this hidden story-within-a-story in the movie, knowing that only a few would ever see this hidden meaning, then he is a GENIUS and Signs stands as an even better movie that I previously gave it credit for.