Let's look at Schroedinger's Cat. If we talked about a multiverse with an infinite number of indistinguishable universes before opening the box, and after the measurement in 50% of those the cat would be dead and in the other 50% the cat would be alive... Then maybe yes. But that would require some form of interaction between the universes and it's not even closely supported by any evidence.
If we talk about the 'Many Worlds Interpretation', in which one universe branches into several new upon each measurement, then this fundamentally violates conservation of energy. Where would all the energy for a new universe come from? If all these universes split and neccessarily drift apart, how comes none of those universes never collided with ours some time after?
Altogether, I will go with 'Wave Function Collapse'.
A collapsing wave function (caused instantly by observation) is a strange idea that is not supported by any evidence. The popularity of the theory seems to be the result of trying to avoid the many worlds interpretation.
The math and detailed background are beyond me, so I have to weigh other people's opinions (rather than the data itself). With that said, it seems similar to Einstein's "God does not play dice with the universe." rejection of probabilistic features of quantum physics.
I also don't think the many worlds is the best answer (philosophically) but that is our best understanding of the data whether we like it or not.