Yes - from the subjective perspective of Schrodinger's cat. Yes - from the subjective perspective of the detector. From the outside we observe the cat's state becoming entangled with that of the radioactive sample, but from the cat's perspective it made the observation, collapsed the state, and either died or didn't.

It's exactly the same for us, making the observation - from our perspective we observed one result or the other, collapsing the wavefunction. But to an outside observer we entangled our own state with that of the cat and the sample, and we're in a superposition of (observed cat dead, observed cat alive) - and will be until they observe us, at which point our wavefunction will collapse to one or the other. And so on.