Was that story part of continuity? Since she has never been mentioned or seen in any
Big Events, I would guess she isn't an honorary or actual Avenger.
Yeah, I really doubt it's in-continuity. The Avengers team we saw in Electric Rain was more like the MCU version than the comics version. The only members of the team that appeared were from the movie (especially the Hulk).
White Fox also got a story in Civil War II Choosing Sides #6 (one of the better stories of the event, imo). Captain Marvel & Agent Brand of SWORD came to her and demanded she join Captain Marvel's side. Carol mentions that they've worked together before. A fight ensued where we learned a bit of history about her. According to history, the Kuminho (9-tailed foxes) typically hunt humans, but White Fox's grandmother changed all that when she fell in love with her grandfather. White Fox is the last of her kind and assumes that the precog (Ulysses) would brand her a threat, so she was appalled by Captain Marvel's side. She also added some Korean global political stuff to support her choice.