Yes. But it’s going to take some backstory for me to explain.
We don’t know the source of consciousness. There is a theory (based on data) that our brains have a quantum entanglement component that would make them un-copyable because you could never recreate the same entanglements. This theory says that once a mind is instantiated in any medium, that medium is fundamental to that mind.
If, on the other hand, consciousness turns out to be a purely classical computation phenomenon, well, first you’ve destroyed any chance at the possible existence of free-will. But, second, if you can map all the zero-one bits in the brain that matter to the computation, then you could recreate it in any medium, even multiply instantiate it.
This brings us to a mid-point idea that allows pulping the brain without loss of consciousness and preserving the possibility of free will. And you can do it without having to understand the existing brain!
Let us assume that there is entanglement in the brain critical to consciousness, BUT all the entangled particles are inside neurons. None of the connective materials that allow one neuron to talk to another neuron are actually critical, so long as the message gets through. Ok, if that’s the case (and it is a long-shot theory), then your nanites could wrap each neuron in a small shell and attach a radio transmitter/receiver. Tune each shell to a different microfrequency and set the receivers to listen on the frequencies of each neuron’s original neighbors. If the broadcast power is strong enough, the neurons will remain in contact even as they slosh around.
There will be side-effects. The person’s sense of time will be disrupted since neurons will have different rates of message delivery at different times. There may be cross-talk with other broadcast systems, and at tiny scale, it won’t take much noise to disrupt the brain. And you’ll need containment to keep the neurons from getting too far apart.
You’re going to need to work on details like a nutritional bath that these neurons slosh in, power requirements, and virus protection. And more. But I think this gets you started. I’m pretty sure this idea — very far fetched though it is — doesn’t contradict any known parts of neuroscience.