I am actually not sure if plain minibatching would work with any MCMC method for that matter. Detailed balance would likely be messed up if different parts of the data are exposed to the sampler at different iterations.
That being said, what can definitely work is a step-by-step updating of the posterior with small subsets of the data. As in, starting with a prior, you expose a small subset of the data to get an intermediate posterior. This intermediate posterior then becomes your prior when the next subset of data is seen, and so on. The problem with this in practice would be to actually specify the intermediate posterior as a prior - it is hard to do so without making any assumptions. One potential way would be to assume that the new prior lies in the same family as the original prior that was specified - then you can take some sort of moments of the intermediate posterior and specify the new prior with that. I do not know if pymc3 has some easy way of doing this, there was a similar discussion with ADVI here: