Re Schrodinger cat, if there are many nuclei which could decay does this lead to multi dead cats?

If a piece of radioactive material is used in the experiment, this might contain billions of nuclei, each of which could decay and trigger the death of the cat. When the box is sealed there is no way of knowing which, if any nuclei have decayed. Does this imply each nucleus can be considered to be in 2 states, ie decayed or not decayed, and for each nucleus does this imply that the cat is also in 2 states, dead/alive.