This is a beautiful question. I think if we look at a human being holistically, the actual organism never dies during the neural replacement. But, in this case, the “you” is referring to your consciousness, your metaphysical being, which is destroyed in the process of your neurons being replaced synthetically. I am not my clone. This destruction of my neurons, to which my experience and being is intrinsically bound, would occur gradually, even if you started with the parts that control reason and memory. The subconscious mechanisms are still you. As long as some of them exist and function, so does some of you. So my answer is that this would be a gradual death.

Other propel have made the excellent point that if the neurons were preserved as they were stripped and reconnected in the same way and continued to function else where, then you never died, your brain was just transplanted.

Can’t wait to see it happen boys! Get your shit together bioengineers and move my brain to a more stable vessel please