For the first initial playthrough, yes (meaning they haven't played the VN before). But subsequent playthroughs are a different matter though, unless there was a major overhaul to the UI at some point. In which case, I could see the player having to not only start over (since there's a chance that older saves would be incompatible), but also have to go through the process of having to select their language of choice.
The dev I work with has had to do that after a major UI/hint system overhaul. Some of the players weren't too happy about having to start over, as you can imagine. But most understand that it's part of the game's development.
That, of course, doesn't apply here though as it seems there were no major changes to the VN, such as the UI.
Point being is that your code should have a checksum that would "look" at the language they selected in their first playthrough and continue on in the same language until the end of the game (meaning a completed version).
At any rate, this is currently how the day 5 script looks. As you can see, it's mixed with English and Russian. Which tells me that they were not translated to English before release. So selecting either language from the main menu wouldn't make a difference (with exception to Russian, perhaps).