I would like to add a little to Lubos's answer:
First a historical note: this is what Einstein proposed as a way of understanding quantum mechanics in 1919 or thereabouts, in the paper "do gravitational fields play a role in the composition of the elementary particles?" Einstein was of the opinion that a complicated enough classical theory, like general relativity, would lead continuous waves to collapse into standard-size soliton-like particles and these particles he felt might then bang around along the wave in such a way to reproduce quantum mechanics.
This idea reappears several times in the literature, but it demonstrably doesn't work. A field theory, like GR, is a classical theory, and it therefore is local hidden variables (the variables aren't even hidden in this case). This is ruled out by Bell's theorem--- the correlations in quantum mechanics don't allow local fields to carry the data that determines the experimental outcome, not without conspiracy (superdeterminism) or nonlocal equations (faster than light changes in the variables). Neither works in a straightforward field theory like GR.
Secondly, GR is not as badly understood as all that, although it is not as well understood as one would like, mostly because numerical methods are in their infancy, and one's intuition must come laboriously from analyzing exact solutions when these are available. The example I gave of particles oscillating into and out of an extremal black hole is not really new (don't give me too much credit), the new thing there is the holographic interpretation, namely that the coming-out is an ordinary coming out event in this universe. The oscillations of particles into and out of a near-extremal black hole were appreciated in the 1960s, but each oscillation takes you to a disconnected branch classically, because crossing a horizon takes an infinite amount of t-time. This is not possible quantum mechanically, since this disconnected maximally extended thing is not compatible with unitarity.
The nice thing about the in-out solution for geodesics in the extremal Reissner Nordstrom is that if you replace the test particle with a little charged black hole, you can make nonrelativistic oscillations if both black holes are near extremal. The external field of the two black holes does not have a full merger, the little black hole, now not considered as a test particle, but as a solution to GR proper, just smears out on the horizon, then bounces back. I didn't calculate this in detail yet, but it can be solved completely with an analysis along the lines of Atiyah and Hitchin in their famous paper on slow soliton scattering (the Atiyah Hitchin space), except here, unlike the other case, I am not optimistic there will be a simple geometrical solution, rather one has to bite the bullet and trace the bouncing behavior in the solution either by numerical integration or solving for the near-static phase-space geometry of the two extremal black holes.
Causalities and CTC's
The basic idea you are giving is that perhaps hidden variables plus closed time-like curves can reproduce Bell inequality violations. I will give some sentences about why this is extremely unlikely.
Quantum mechanics has entangled wavefunctions. What this means is that the wavefunction for k particles is in 3k dimensional space, not in 3 dimensional space. The growth in dimensions means that quantum mechanics packs a stronger computational punch than classical mechanics, and you can't simulate quantum mechanics of k-particles with less than exponentially much classical information. This is why quantum computation works in pure quantum mechanics.
So the structure of quantum mechanics is exponentially big and has the entanglements that violate Bell's inequality. If you wish to reproduce this from something like GR, you need gross nonlocality and some way of reproducing nonlocality.
So if you have a pair of electrons that bind to an atom (so that their spins anti-align), and then you knock out the nucleus, and do Bell measurements on the two outgoing electrons, you need to reproduce the nonlocal correlations from CTC's in GR. This means that the electron needs to have CTC's "inside" which go back in time and magically alter the attributes of the other electron. This only became required once you put them together in an atom, and let the photons radiate, and during this process the two point electrons didn't necessarily come close to each other (assuming they are classical and described in space). How do CTC's help correlate them?
To make this work, you would have to go all the way back in time to where the two electrons were created from the inflaton field, and correlate them back then. This type of back-and-forth in time description is utterly conspiratorial, and very unconvincing. There is also no shred of a hint that this will reproduce anything like QM, it's just not ruled out, because you are postulating little tiny internal back-in-time paths on all electrons, something we have no evidence for.
There are no real CTC's in physical exterior solutions of GR. The CTC's in the intepretation I gave of oscillations into and out of extremal black holes are unphysical--- they are only closed in time because of the wrongness of the classical picture of the horizon.
The CTC's in the interior of a Kerr solution can only occur when you wind around the ring singularity, and then it should be possible to unwrap the interior so that it has a pure-causal description, simply by including the winding number of your path around the ring. I don't know the interior Kerr well enough to see how to do this, and this must work in any number of dimensions, not just 4, so I hesitate to say it is what happens, but there must be a reconciliation of causality and Kerr interior, because you can set up fields at the horizon of Kerr, and let them traverse the interior, and the evolution equation shouldn't have additional constraints, as come from CTCs.
All in all, the form of the two theories, GR and QM, is completely different, the descriptions are of a different computational complexity, and the causality notion is totally different in the two schemes, so it is implausible in the highest degree that GR can explain QM.
What's more, today we have a good quantum version of GR, string theory, which subsumes and extends the classical theory, so that it is a mistake to pretend that this progress does not exist, and to work as if we were living in 1926. Within string theory, you give a full accounting of all GR effects on flat and AdS backgrounds in principle, from an ordinary unitary quantum theory. This quantum GR means that we know how GR and QM are reconciled (in perturbations to flat and AdS backgrounds), and the classical limit where GR is reproduced is just not quantum, it's an ordinary classical field theory.