I've tried that twice without much success, though I still like the concept.
1. Modern corn is shorter and has thinner stalks. They may need some support.
2. Modern squashes don't like to climb much. You may want an OP variety.
3. Pole beans can take over the corns. But I like flat italian ones so that might make a difference.
Best of luck and I hope to see a great 3 sisters garden. You'll never know if you don't try it...