I think that Elizabeth really was dead when Julia pronounced her dead. Granted, at some point during all this we heard Elizabeth's thoughts when she was supposedly dead - but her spirit was a separate entity from her body at that point. It was in the same place, but it could not have dependent on the body, because there was no way for the body to support it. All tests on Elizabeth would have come up negative except for one: time, which showed that the body did not decompose. But the non-decomposition angle was saved for another storyline.
Looking over this post, I'm thinking that it was out of character for Julia just to forget the whole business when Elizabeth eventually came back to life. She told Barnabas in episode 291 that she was interested in the line between life and death. Or something like that. It's conceivable that (contradicting my earlier assertion) during all the time that Elizabeth was believed to be dead and was not breathing, eating, or eliminating matter, there was something in Elizabeth's body that was alive - but what could that something have been? Julia should have been eager to investigate the mechanics of Elizabeth's experience.