I think this depends on the answers to problems in anthropics and consciousness (the subjects that no one understands). The aptness of your thought experiment depends on Everett branching being like creating a duplicate of yourself, rather than dividing your measure or "degree-of-consciousness" in half. Now, since I only have the semipopular (i.e., still fake) version of QM, there's a substantial probability that everything I believe is nonsense, but I was given to understand that Everett branching divides up your measure, rather than duplicating you: decoherence is a thermodynamic process occuring in the universal wavefunction; it's not really about new parallel universes being created. Somewhat disturbingly, if I'm understanding it correctly, this seems to suggest that people in the past have more measure than we do, simply by virtue of being in the past ...

But again, I could just be talking nonsense.