I am using a a Pyro Bake Volume node to shade an explosion. This seems to replace the Pyro Solver node's own shading system (Pyro Post Process node) -- do I have to deactivate the Pyro Post Process node, or is it just overridden automatically?

If you had enabled "Assign material" in the Pyro solver, Pyro Bake Volume will override that with a new material, and possibly create new VDBs its material needs. However, everything in Pyro Post Process (converts, culls, resamples...) will still apply. So no, no need to deactivate anything.