Good points, Dave.
I have my own thoughts regarding the matter, but they're based solely upon semi-educated guesses.
To start with, we retain our sense of 'self' despite the fact that the cells of our bodies, and even the atoms themselves, are constantly being replaced by new ones. I doubt that there's one single atom left in my body that was a part of me when I was born.* In that light, I think that if the engrams of someone's brain could be successfully duplicated in a computer, that 'model' would indeed be conscious. That wouldn't present a problem if the original is destroyed. If, however, one or more duplicates are made, whether or not the original survives, each would think that it's the real 'person'. The restriction of movement, perception, whatever imposed by being part of a machine would be definite evidence of its true situation, but it would still have that sense of 'self' as well as all of the original's memories up to the time of duplication. From that moment on, they would all become distinctly different 'people' due to differing experiences. If the biological unit no longer exists, who can say which is the 'real' one?
*I saw written somewhere that with every breath you take, you inhale several million (or billion?) atoms that were once part of Julius Caesar's body. The same can be said for anyone else that has lived on the planet long enough for those atoms to have dispersed completely. In that sense, we all still have a lot of our original atoms, but not likely in the same role that they played the first time around.