Your consciousness uploaded and then downloaded into a synthetic human like body isn't ever going to be you. As the man said “transhumanism is a warmed-over Christian heresy”.
The Ship of Theseus is the warmed-over Christian heresy. A brain is an organism with a symbiotic tight coupling to a meat bag, and the brain itself a similar cooperation by accident.
An organism can develop that builds new tight "synthetic" couplings; it isn't sci-fi. It's partially released today. It's just that we are so normalized to the interfaces of smart phones, keyboards, monitors, steering wheels, and so on that we didn't notice it's arrival.
More exotic, more tightly coupled interfaces also exist today (there exist direct-to-brain interfaces that provide a new sensory feedback loop that you brain can adapt to), they're just not as competitive currently with thousands of years of neural optimization of hands/eyes/nose/touch.
Why would you want to do this? Who knows. Why do we want to do anything? Maybe a person wants to be part machine as a lizard-brain driven reaction to a low-oxygen office environment that sees no viable way out.
If I replace a single one of your neurons with a mechanical replacement, are you still you? What if I replace half? All?
If you walk across a room, are you still you? What if I break you down, and reassemble you at the other side of the room, using the same atoms? What if I only use half the original atoms? What if I freeze you, move you across the room, and then dethaw you?
As far as I (crudely) understand it, we don't know what exactly the cause is, other than it's tied extremely tightly to the brain and seems to be an accident of evolution/an illusion.
My guess is that as long as the neurons keep firing continuously and the illusion is unbroken, the "you" that is you right now will remain you. So you may well be able to go full ship-of-theseus and piece-by-piece completely replace the physical layer without breaking the consciousness, but if you stop it completely with an upload/download* , continuity is broken and the new "you" will be an exact duplicate while the "you" right now will cease to be. Because it's an exact duplicate there would be no way to confirm this, though - the new "you" would think it had continuity due to how complete their memories are.
* I'm thinking of switching to a robotic brain all at once here, instead of piece-by-piece. I'm not going to touch a transporter as suggested in your comment, as that probably depends on technical details of the transporter for what exactly is going on.
I think that conventional notions of identity are probably incoherent, and mean you die from second to second anyway.
I'm not likely to have the same reactions after lunch that I had before lunch, or consistency from yesterday to today.
Can it be done in a way that doesn't imply the death of the subject?
The key word is replacement. Can this replacement vote or inherit property? What happens if there is a clerical error and they make two replacements. Which one is the real you?
Incidentally, this is why I can't take Roko's Basilisk at all seriously - a future simulation of me is not me. Well, it;s one reason anyway.