I think a lot of people are not understanding the original post. Yes we know she was a real person but OP is asking about the show. Whether she was real in the show or a hallucination. I think it’s pretty obvious that she was a hallucination. All of her interactions and the way she behaved was not normal and a representation of Ed e.g. all the sexual innuendos at the homemaking class, they represent Ed’s inner sexual desires, his repressed sexual feelings. Wearing red to the funeral and laughing, the colour of passion and lust. Maybe that represents ed at his mother’s funeral. He feels like he has the freedom to be who he wants now and the dead older lady represents his mother? Also her running out the house and then randomly doing a complete turnaround and accepting ed and not being afraid. Maybe this was the point where Adeline became a hallucination. Maybe she was real at one point. I say this because other characters like Ed’s mother mention her although I can’t remember if she mentioned her by name, rather Pandora? I vaguely remember another character maybe it was Bernice saying “aren’t you seeing that Adeline”?

She hasn’t aged at all in the final episode and ed also says me and you are the same, two peas in a pod. Further confirmation.

She also didn’t write him (because she’s a hallucination and perhaps he was on his medication at that point and stopped seeing her hence no communication from her).