I don’t think there was ever a real school that remotely resembled the CS — certainly EBD’s own school wasn’t!
Realistically, even if a real Madge, Joey, Simone and Mademoiselle had started a school on a remote Austrian lakeside in the 1920s, it would have been likely to stay a very small affair, possibly augmented in summer by the daughters of people with second homes at the Tiernsee, and wouldn’t have continued after Madge’s marriage, or, if she didn’t marry, after Joey left school and was making her own way in the world (as she’d have had to, presumably, if they were still poor, rather than just living at Die Rosen, continuing with her singing lessons and helping out with the babies?)
The fate of the Saints always seems rather more probable!
It’s an interesting question — what would Joey have done if she’d needed to earn her own living immediately after leaving school? Stayed on at the CS to teach? (Would her grades have been good enough to get her a place at a teacher-training college or university?) Trained as a singer? Gone to India to live with Dick and Mollie and discreetly search for a husband?