Vulkan will not have the CPU-time performance costs associated with state changes (validation overhead, etc). But Vulkan command buffers do have state. They have two very major pieces of state: descriptor sets and the pipeline object.
Both of these objects are monolithic, dealing with potentially lots of pieces of information. The (potentially) huge quantity of stuff these objects control should strongly suggest to you that binding new objects is not cheap. And that's in terms of GPU execution speed, not CPU validation or whatever else.
Vulkan in general tries to make slow things in the API look slow and fast things look fast. Render passes are big, huge and complicated, so clearly you shouldn't just be starting and stopping them whenever you feel like it. Pipeline objects control a huge amount of information, so binding new ones feels like a heavyweight operation.
By contrast, changing what buffers get used for vertex input feels like a short, quick, focused operation. So it's probably cheaper than changing the pipeline that uses those buffers.
So yes, you should avoid state changes in Vulkan, just as much if not moreso than in OpenGL (since many state changes in Vulkan require entirely new pipelines).