Regarding computability, I wouldn't dare giving any opinion on that, and hopefully didn't in my original post. All I'm saying that once we figure how information is stored and processed, with enough technology we could replicate the process. It's not about computability- if you are making a biological duplicate I'd expect it to work the same way. Some might say this is not the "singularity", but it walks like a duck, quacks like a duck...

Also, it would help creating silicon equivalent. Imagine we have something just as small (or smaller) than a biological neuron, which can interface and work in the very same way.

Computability or not, if it works in exactly the same way, I'd guess it could work the same on a higher level too - like, in a brain, especially if we have figured how to extract the stored information and if we can feed it back. (unless there are emergent properties we missed in the first place, but then if they can be identified, maybe they can be replicated too?)

That would allow an iterative trial/error (ex: if it doesn't work - why?) which might not resolve the computability question, but bring even more interesting issues about why it might not possible - something we can learn only from an experimental approach.