Definitely not. Georgiana Cavendish's name is not associated with the field of novel writing. It's possible she was involved in different forms of creative or intellectual pursuits, but not novel composition.
Well, perhaps they could become instant friends. Elizabeth might be charmed by Georgiana's shyness and gentle nature, and Georgiana could be drawn to Elizabeth's lively spirit.
She might survive by making use of her relationships. For instance, if she has some sort of connection with Loki (maybe from past encounters), she could call out to him telepathically (if there's some sort of magic involved). Loki, being the trickster he is, could then come and rescue her. Another way is that Darcy could use her knowledge of science to create a makeshift weapon or a device that would help her escape from Hydra's clutches. She could use the materials available in her cell to build something useful.
In literature, one of the most famous Darcys is Fitzwilliam Darcy from Jane Austen's 'Pride and Prejudice'. He is a complex character, initially seen as proud and haughty, but as the story progresses, we discover his true and noble nature. He falls in love with Elizabeth Bennet, and their relationship is full of misunderstandings and growth.
In a fanfiction, Darcy could be wearing special glasses that allow her to swim underwater for a long time, like some kind of high - tech Avengers gadget. She could be using this ability to spy on an underwater threat. The other Avengers might not be aware at first, and there could be some comical misunderstandings.
They might start with a cautious acquaintance. Georgiana, being a bit reserved, would probably be polite but a bit shy at first. Elizabeth, on the other hand, would be friendly and curious.