The short simple answer is no.
The long more complex answer is that the death of the author is contextual. It depends on the purpose of the work, as some exist outside the author, while others incorporate the author into the mythology of the work. Hideaki Anno is no different. In Japanese, family names are placed before given names so for the remainder of this essay I will use his given name, Anno. The more he tries to distance himself from his work, the more he becomes part of it. This is in contrast to J.K. Rowling, where the more she tries to be a part of her work, the more people want to distance her from it, but in doing so, she is still being incorporated into the mythology of the work. Just not in the way she hoped for. H.P. Lovecraft, very much a product of his age, is also deeply problematic by the standards of today because of the ethnic and gender stereotypes he embraced, yet he is deeply influential in film, tv, literature, and other mediums, so even though he died in in 1937, as an author he lives on.
Neon Genesis Evangelion is considered by many to be a seminal Anime. The Anime examines things like depression, existentialism, life, death, love, abandonment, and the precociousness of youth. Every single character has some deep emotional scars.
Anno has had depression for a long time, (Nivenus, 2020), and feels that he is emotionally stunted because of the youth he feels that was wasted on things like Anime. The irony is that he, and GAINAX, the studio that created and produced Neon Genesis Evangelion, is considered one of the greatest creators of Anime. As such, it could be argued that Neon Genesis Evangelion is an exploration of emotion and philosophical standpoints, and self-referential of its creator, even though Anno states that ultimately it means nothing (Idea, 2020). If that were the case though, it wouldn’t exist. By saying that the series means nothing, Anno invites the audience to watch and dissect the series to garner a meaning of their own, which would signal that he is distancing himself from the work and allowing his authorship to die. In contrast to the concept of the death of the author though, his continual interactions with the fan base further entwine him into the mythology of the series thus preventing the death of authorship.
Neon Genesis Evangelion was carefully constructed so that throughout the series, two of the main characters of Shinji Ikari, and Asuka Langley Soryu shift several times emotionally psychologically and philosophically, as do several supporting characters. As Anno says, all the major characters of Neon Genesis Evangelion are broken in some way.
Shinji Ikari, a 14-year-old boy was abandoned by his father, Gendo Ikari, at a young age. Shinji’s only interactions with his father since childhood have been fundamentally utilitarian. If Gendo has no use for Shinji, Shinji is sent away and his existence ignored. When we first meet Shinji, he is arguably apathetic. He exists but doesn’t care that he does, knowing that he is just a utility for his father, Gendo, to use when he is needed and packed away in a proverbial closet when he is not. Due to social isolation and abandonment by his father, Shinji has a hard time making friends, and when he does find acceptance amongst his peers his spirits lift marginally until he is forced to watch as one of those friends are killed. This sets Shinji on a downward spiral. Furthering his decline, when Asuka sustains a serious injury for which he blames himself, he finds himself trying to rouse her from a coma, accidentally exposing her breasts. This leads to further self-loathing and steeper decline of self-worth when he comes to the realisation that he has masturbated over the body of an unconscious teenage girl. This steep decline continues until he is forced to personally kill another friend which causes him to shut down mentally emotionally and psychologically until finally his psyche is shattered beyond repair. I think that for most of the series, Shinji falls into the category of existential nihilism in that his actions show that he believes his life having no meaning or value.
Asuka, also 14, on the outside at least, is the polar opposite of Shinji. Sure of herself, overachieving, overconfident. In many ways, she is the embodiment of the toxic ego. The Narcissist. Until she is defeated in battle. Not just once but several times. Each defeat chipping away at her ego until she too has a complete mental emotional and philosophical shutdown. Unlike Shinji, Asuka is an orphan whose issues do not stem from being a utility of her father but instead stem from witnessing the suicide of her mother for which she blames herself for not being a good enough daughter. Asuka snaps out of her depression in the last episode when she finally arrives at the realisation that even though she has felt alone for many years, she never truly has been alone. She is then killed. This is the event that finally and irreversibly shatters Shinji’s psyche.
This up and down of mood and self-loathing is common amongst people who have depression, such as Anno and I, and like Shinji and Asuka, there are triggers that send an individual into a depressive episode and triggers that snap the individual out.
So no, I do not think Neon Genesis Evangelion signals the death of the author, there is just too much of Anno and to a lesser extent, GAINAX, woven into the story. In this case, for as long as the work exists the author will never die.
Idea, P. (2020, 11 9). Does It Matter What Evangelion’s Creator Says? Retrieved from Youtube: https://www.youtube.com/watch?v=SVm65tlhqw8&feature=emb_logo
Nivenus. (2020, 11 9). Insufficient Direction: Or How to Stop Worrying and Love Otaku Culture. Retrieved from observationdeck: https://observationdeck.kinja.com/insufficient-direction-or-how-to-stop-worrying-and-lov-1678079058#:~:text=A%20long%20sufferer%20from%20depression%20and%20low%20self-esteem%2C,Godzilla%29%20and%20as%20a%20result%20feels%20emotionally%20stunted.