I think (modern) rat poison works by mimicking vitamin K thus inhibiting digestion of actual vitamin K. This in turn will lead to internal bleeding and therefore the rats death. So if you eat enough of it or are small (like children) and decide not to seek a doctor to stop the symtoms it can defenetly kill you, albeit slowly and painfully.

You could however save money, since this kind of rat poison is not really biodegradable and sticks around in its victims and their predators. So just eating a dead rat would be cheaper and might have the same effect.