My hunch is that CDCL is probably the wrong approach to take for parallelization due to synchronization issues. You want an algorithm that is communication-free or makes belief propagation wall-clock competitive for large set of instances. It should be possible to modify BP to be asymptotically complete by using a special-purpose PRNG that ensures samples are drawn uniformly without replacement from the search space, but I'm not sure how to make it more sample-efficient.
They are not friends with bottlenecks like clause queues used in contemporary stochastic SAT solvers.
They can be good at something like survey and/or belief propagation [1].
[1] https://simons.berkeley.edu/talks/belief-survey-propagation
The problem is that survey/belief propagatin is effective in the area of random CNF problems and it is not a complete solution technique. It may compute a solution but it cannot provide you with the evidence that there is no soolution.