That “trick” works for MCMC sampling, but wouldn’t be applicable to VI (there aren’t even step samplers there).
I am not sure whether VI allows you to infer the posterior of some variables, while keeping the prior for others. I don’t even know if it makes conceptual sense in that context.
If it does make sense, perhaps Minibatching across the histogram of the “fixed” variables achieves something like what you want?
Maybe @ferrine or @fonnesbeck can weigh in?