Can a school exist without curriculum?

No, a school cannot exist without a curriculum, at least not in any meaningful sense. A curriculum is a plan or framework that outlines what will be taught and learned. Without a curriculum, there would be no structure, no goals, and no way to measure student progress. The students would essentially be unsupervised and the school would lack purpose. While the specific form of the curriculum might vary (e.g., very unstructured, heavily project-based), some kind of plan for learning and teaching is essential for an institution to be considered a school.