Actually, this would be like the case where you shine a light in the two-slit experiment to see which slit the electron passes through, but the light is dim enough that it won't interact with the electron every time. You get the sum of an interference pattern and a classical double Gaussian in that case.

In the experiment you suggest, the experimenter's wavefunction would be the sum of one where the cat is dead and the experimenter observes a 1, and one in which the experimenter observes a 0 and the cat remains in dead-alive superposition from the observer's perspective. (That is, the weighted sum of a factorizable wavefunction with a non-factorizable one.)