The one other story I did it for it kept the characters quite well for the key characters, and then some of the minor characters deviated somewhat. But that one did have a lot of characters and spanned a quite long "in-game" time. For Galatea, the story is quite tightly scripted, with few characters, so I would think it wouldn't be too noticeable.
In summary, I think it depends on how much the game book defines and describes the characters, the overall tone of the story, as well as how the save summary is written. You could also consider instructing the GM/AI specifically to focus on retaining the feel of the characters in the save game OCC.
TheGalateaProject
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Tips: Out-of-character (OOC) messages, and other ways to use your AI GM comments · Replied to dudusaiko in Tips: Out-of-character (OOC) messages, and other ways to use your AI GM comments

Link: https://thegalateaproject.itch.io/the-galatea-incident
An AI-run fully fledged narrative story.
The MC encounters a dying stranger who injects him with something to hide it from pursuers. The next roughly 14 days he has to navigate a brand new existence in order to have a shot at getting his life back. The game features a highly customizable, but strictly structured story with multiple endings and variations of these depending on the choices of the MC, especially in relation to his partner who also finds herself in the toughest two weeks of her life.

