>>719913968
I think the crux on that question lies in what you consider "you", as they usually do.

>"You" are the processes and functions your neural network create
Would still be "you" in your question.
>"You" are your neural network
In this case, "you" would indeed disappear, replaced with a facsimile of "you". I'd say that to believe this, you'd have to believe there's another factor that makes your biological neural network something distinct, even if you'd behave exactly the same if your entire neural network got nanomachine'd.

It's as >>719914225 says, a lot of us gets replaced day by day, cell by cell. I can't speak confidently of our grey matter, but the rest of the body, what was it, is on average fully replaced in about 7 years?
A quick cursory google search says neurons carry DNA. If artificial neurons carry DNA, I'd say they can constitute "you" if they were a perfect copy. DNA is an RNG seed anyway.
In that sense, I'd consider it reasonable if someone were to deny that "you", your neural network, dies when it gets replaced, since your RNG would be all out of wack despite still using the same seed. If that makes sense