Even given the general hypothesis, most of the brain's computations are still being done classically and unconsciously, in the form of interactions among small quantum systems (environmentally decohered biomolecules, let's say). Snipping through a bundle of nerves will interfere with these classical computations and have functional consequences.

But I really have nothing to say about split-brain phenomenology from a quantum perspective. The big biophysical challenge for me is just to explain how you can have significant structured entanglement extending beyond the individual neuron. How might the electrons (say) in one neuron even become entangled with those in another? The quantum-mind literature has suggestions, such as phonons in the polymer fibers of the extracellular matrix.

But I would prefer to first see much more progress in understanding the quantum dynamics of living matter when investigated from a neutral perspective, one that isn't specifically looking for interneuronal conduits of coherent quantum interaction. We need to know whether proteins spend significant time in superpositions of different conformations, whether the aqueous intracellular environment is entirely thermal or contains any form of quantum order... There needs to be a little more progress in general quantum biology before we can have a well-founded quantum neurobiology.