To my knowledge, it does not. There are various items to address with only item 4 being currently with no clear direction:

1) Bohmian mechanics seems to require some kind of simultaneity. Various proposals have been put forth for making natural foliations, possibly using the wave function to do so, that allow one to evaluate the positions of all the particles at a given time so as to know which configuration point to use in obtaining the velocity of the particle. This is possible, but it does not feel philosophically satisfactory yet. GRWf does not require a foliation to be relativistic which is a nice feature.

2) Quantum field theory naturally models particle creation and annihilation. Most QFTs are presented in a mathematically incoherent way. While conclusions can be made via renormalization, etc., driving an actual dynamics is tricky from that stuff. By not doing perturbations but rather defining the operators by taking into account the shifting of the probability from one sector of n particles to another of n+1 particles, QFTs can actually be made to make mathematical sense. This has been accomplished in some of the simpler models. It is not a problem whatsoever to define a Bohmian evolution where particles appear and disappear in a probabilistic fashion. The difficulty is purely in having a properly defined wave function evolution and that is on its way to being solved.

3) One needs to define wave functions, their evolution, and the particle evolutions in a curved space-time. This is not a problem whatsoever. It is very easy to translate and interpret what we need into differential geometric language. QM has issues with the usual observables/operators translating (such as a momentum operator), but since these are derived concepts in Bohmian mechanics, no fundamental difficulty arises.

4) In general relativity, the mass distribution is part of the evolution of the space-time metric. The mass is based on where the particles are. To date, the wave function tells the particles what to do, but the particles do not have any impact on the wave function. The wave function is impacted by the space-time metric. Also, there are some suggestions that mass might be entirely a part of the wave function and not associated with the particle, i.e., the particles are really just undecorated points moving about.

Basically, gravity and the wave function need to work it out and the particles will then be guided by both as the space-time metric is what takes the gradient of the wave function or, for Dirac style motion, something analogous to a square root of the metric is floating around. Bohmian mechanics does have the advantage that it just has to be concerned with the evolution of the particle lines and not having to figure out how to define various observables.

In other words, a known space-time metric interfaces just fine with Bohmian mechanics, but figuring out how to evolve the space-time metric is still an open question.

At the current time, I am not aware of any novel ideas coming from a Bohmian or GRWf point of view towards resolving the problem of gravity.

If interested in a good discussion of all these things and much, much more, I highly recommend the recent book Foundations of Quantum Mechanics by Roderich Tumulka which covers what the title says, but also discuss Bohmian mechanics and other interpretations.