The problem with this scenario is just what I said in my original reply: the very nature of her death.
She was burned at the stake. There wouldn't have been very much of her left to restore.
I severely doubt the elixir could recreate a person from blackened ash, no matter how salubrious it was!
If they were going to include her, they would have to alter the circumstances of her death or (more likely) pretend it never happened. Now this is plausible in a world like this, since it is an alternate history. Just seems a little more difficult given how famous and legendary the death of Joan of Arc is.
Also, I don't think the characters in The Order are truly immortal per se. They clearly still age, just at a incredibly diminished rate. I don't know how effective the elixir is to keep a person like Joan of Arc alive into 1886. That would be like 450+ years after her death.