She will survive anon, and if Armin says that Annie is trusthworthy, Hange will believe.
I think that once she got out of the crystal, Annie will go to Paradis side because Armin will convince her to fight with them.
Then he will say something like "I'm sure we will be able to protect your father too", then she will tear up a bit and hug him while crying tears of joy. "T-thanks Armin-sama! A-Armin-sama... AISHTERU!!"