And even if you do, then the only viewpoint you will have really falsified is one which postulates that (a) the state vector collapse is caused by consciousness, and (b) concludes that therefore any consciousness has to do the trick, even one simulated on a quantum computer. I have met exactly zero physicists who'd treat (a) seriously, but even if you believe in (a), (b) still doesn't need to follow (someone could believe that only real human brain makes the magic happen).
(I assume you were referring to experiment 3. from Deutsch's "Three experimental implications of the Everett interpretation in Quantum Concepts in Space and Time.")
Sean Carroll, physicist and proponent of Everettian Quantum Mechanics, has just posted a new article going over some of the common objections to EQM and why they are false. Of particular interest to us as rationalists:
Very reminiscent of the quantum physics sequence here! I find that this distinction between number of entities and number of postulates is something that I need to remind people of all the time.
META: This is my first post; if I have done anything wrong, or could have done something better, please tell me!