I thought the irony of the tsundere archetype is that Asuka codified it without being one herself.
Also the other irony is from a study I read a few years ago about how first meetings influence your opinion on people, that concluded by saying that we respond best to and feel the most warmly about people with whom we had a difficult first meeting with and then a progressively slowly improving relationship. Translation: we have a psychological bias towards the melting tsundere plotline, in real life.
But no, Asuka's not really tsundere, she's poorly socialized from never being around people her own age, traumatized from her mother's insanity and death, and a bit of a misandrist thanks to her father betraying her mother. Maybe most importantly to her on-screen interactions with Shinji, Asuka's taking cues on how to be an adult from
Misato.
Copious junk food, messy eating habits, skimpy homewear, complex about the men in her life? Hello Misato 2.0.
EDIT: Thinking about it, that really could be where Asuka's crush on Kaji comes from. Misato's an adult woman who Asuka respects, Asuka wants to be an adult woman, Kaji is Misato's ex, if Asuka can land Kaji she'll be as much a woman as Misato, and better if Asuka can keep him.