It’s difficult to consider this, even speculatively, beyond the realm of science-fiction. However, in terms of the traverse of information and the search for truth, these concepts could potentially be an underused search function.
… unless that’s too much of a stretch. 
If assumtions are sound, I doubt this could be proved; period.
Looking at black holes, as a model: Once information has passed the event horizon, destined for singularity, that information is lost; irretrievable. This is one of the fundamentals, as I understand it, that allows and predicts the existence of black holes, within the framework of general relativity.
Now, we have proof that black holes are not only possible, but are numerous; most, if not all galaxies have at least one black hole at their core. Interesting in itself, if you consider them as counterweights to expansion.
“Nothing can escape a black hole; not even light” – that’s the inescapable inference of everything we have learned about black holes. Fine.
Let’s move on to quantum entanglement. Firstly, we note that QE aka spooky action seems to violate the FTL prohibition; from the perspective of special relativity. Simply stated, information can not travel faster than C (lightspeed).
Within the MWI, when two particles are entangled the combined state becomes a superposition of all possible outcomes; each corresponding to a separate branch of the multi-verse. Now, the MWI also maintains that there is no superluminal communication between parallel branches of the multi-verse; meaning, that information can’t travel from one branch to another (any faster than C). Subject to the physics of spacetime the escape velocity, if you will, of any given branch, would need to be in excess of C.
From the perspective of any one branch, measurement of an entangled particle seems instantaneous. This is due to the correlation of entangled states; each branch is independent and evolves separately within its own spacetime.
The MWI is then consistent with special relativity in that no information is transmitted faster than C within any particular branch of the multi-verse – the apparent perception of non-locality observed [arguably] becomes due to the existence of multiple fractures of spacetime; and by extension, the multi-verse.
Extrapolation:- if the MWI does not inherently violate special relativity; or the FTL prohibition, this means (in a nutshell) that we can’t possibly know of the existence of the multi-verse; because akin to black holes, no information can traverse the event horizon or a similar boundary, if it exists.
This is the point where speculation leads to the EPR paradox; and where science-fiction takes the lead – time and relative dimensions in space; wormholes, and such.
E&OE.