If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.
On the conditions of the "Schrödinger's cat" thought-experiment, as presented in The Present Situation in Quantum Mechanics (1935), translated by John D. Trimmer