Of relevance here is this previous post where @junpenglao notes that this dropout is a model fitting technique.
If I were to perform Metropolis sampling on my mu variables based on sample/draws/proposals of d from the Bernoulli prior, I would be performing monte carlo integration as part of my posterior sampling scheme. As a strategy, with a (quite wide) uniform proposal distribution for mu, this could overcome the posterior symmetry identifiability that is the more standard MCMC techniques will not address (as they will generally be get stuck in one of the symmetric posterior modes), but it will not address the fact that this model specification is a “selection prior” not a “dropout” specification.