It doesn't sound like it doesn't rule it out, but also doesn't provide a way of testing it against other interpretations of QM.

I don't thin it would even rule out non-local hidden variable interpretations of QM such as de Broglie–Bohm theory <http://en.wikipedia.org/wiki/Bohmian_mechanics>, since these accept the wave function as real but posits that there is also an actual configuration of the universe, which evolves in a manner that is guided by the "pilot wave".

Page 4:

"On a related, but more abstract note, the quantum state has the striking property of being an exponentially complicated object. Specifically, the number of real pa- rameters needed to specify a quantum state is exponen- tial in the number of systems n."

This is an oblique way of saying that (quantum) reality consists of many (classical) worlds.

No it isn't, it's an explicit way of saying that the number of real parameters needed to specify a quantum state is exponential in the number of systems.

Why do you think those are mutually exclusive? "the number of real parameters needed to specify a quantum state is exponential in the number of systems" is just a rewording of "the quantum state function is an exponentially complicated object." But when you combine that statement with the main point of the paper, namely, that this exponentially complicated object is physically real, it is not unreasonable to infer that this physically real exponentially complicated object comprises multiple copies of classical reality.

In fact, there are logically only three possibilities:

1. The quantum wave function comprises zero classical realities, i.e. what we call classical reality is not real but some kind of illusion. This is actually a scientifically tenable point of view. See http://arxiv.org/abs/quant-ph/9605002, particularly section VI.

2. The quantum wave function comprises one classical reality, i.e. Copenhagen. This is not any more a scientifically tenable point of view.

3. The quantum wave function comprises multiple classical realities, i.e. many-worlds is (are?) physically real.

Personally, I subscribe to option 1.