In the naive way of making a copy of it, yes.
But consider this: with some future procedure, each neuron of your brain is replaced by a mechanical one, one at the time. You maintain your consciousness at all times.
In the end of the process, you now have a fully mechanical brain.
No philosophical conundrum this way, right?
>The universe eventually dies, too. 10 billion years is not immortality.
Yeah, I don't care, 100-200 million years sound enough for me until I get bored.