I think the brain is probably ultimately computable by a classical computer and yet quantum computing in the brain might be significant. Here are couple of the potential problems we'll have if the brain relies on quantum effects.

1) Difficulty in replacing bits of the brain functionally. If consciousness is some strange transitory gestalt quantum field; then you would need to to make a brain prosthesis that had the same electromagnetic properties as a neuron. Which might be quite hard.

2) A harder time simulating brains/doing AI: You might have to up the date you expect Whole Brain Emulations to become available (depending upon when we expect quantum computers to be useful).