What will happen to the additional CSS when the theme is updated?

Nothing. The Additional CSS section of the customiser will be unaffected by updating the theme.

The reason you may have seen warnings regarding updating themes and losing customisations is because when themes are updated, all of its files are replaced with fresh copies. So the reason you lose changes is because if you modified the themes files then they have been overwritten with copies that don’t have your changes. None of this is relevant to the Customiser, because it doesn’t modify theme files.