Honestly, that's kind of the simplest way to describe Jane LA. There's so much more to it than that question and in a way, the film uses that trope in order to reel you in to the narrative and then breaks it down. It plays with the audience's expectation of who Jane is but then turns it around on them by the end. Jane LA guides us through the mind of an anti-hero uses the Manic Pixie Dream Girl (MPDG) trope as a lens.
Right at the start of the film, we can already see the way the MPDG trope fits into the narrative of this film. We meet Jane, she's shooting off fireworks in the alley, laughing, smiling, and joking with the director Trey (played by actual director Max Landis). She comes off as bubbly, cute, and quirky.
These early scenes are important because they set up the audiences expectations of who Jane is and what her motivations are. The feeling we get from Trey through the way he asks the questions is that he doesn't (the same way we don't) believe someone like Jane really wants to build a bomb (did I forget to mention that part? Jane wants to build a bomb and kill a lot of people). We, like Trey, are along for the ride but don't believe anything will come of it. That sentiment is also reflected in the portions of the film that focus around Jane's friends.
The message that's being sent is that they don't believe her, Trey doesn't believe her, why should we?
It isn't until Trey enters Jane's house after she's done mixing chemicals that things become real for both Trey and us, the viewer. Trey's reaction mirrors ours, the early portions of the film set a tone that's lighthearted and, maybe even, fun. It's at this moment that everything becomes real for Trey and the audience.
We/Trey start to believe that Jane is actually capable of what she says she wants to do. But, even then, there's still a little bit of hope that Jane isn't the type of person who will bomb a heavily populated area.
Even though she's initially presented as MPDG, it slowly becomes clear that she isn't. There are multiple moments throughout the film where she states how alienated she feels from the rest of the world. We learn that she's motivated by creating a connection between people, she believes that society closes themselves off to others and the only way to connect people is through a disaster.
So, honestly, after watching the film over and over again. I'm not sure if the film answers the title question of this card. Because Jane isn't Tyler Durden and, to me, she isn't a Manic Pixie Dream Girl. Jane is Jane. Her motivations and her actions are her own.
Also, the film has an entirely different message if read the proper way. Sure, it's under the guise of nihilistic whismy and explosives but part of me sees that this film is sending a message that says, "if someone tells you something about themselves, you should believe it instead of question it."
That's probably as vague as I could put it without inciting any intense arguments but if you unpack the narrative of the film, it's solely based on the idea that Trey, Jane's friends, and us (the audience) don't believe that Jane has the capacity to set off a bomb in a public place. And we don't believe it because of the way she comes off/the way she's portrayed. And even now, I can think of times where certain people weren't trusted on their word because of the way they come off to the public (again, I'm being vague on purpose).
Jane LA plays on societies expectations of people and they way they are perceived in order to get its message across. And without our, honestly, horrible stereotypes this film wouldn't be as intriguing to me as it is.