No matter how many times I say that I'm speaking from the individual's point of view, some readers seem incapable of looking at it from an individual perspective.
In the case of your statement, it would solely depend on how the copy was made. If it's copied by somehow reading the consciousness, storing it as data, and perfectly restoring it in a new brain, then no, it is not the same consciousness, and from your perspective you are dead.
If it's copied through some kind of direct transfer, where the electrical impulses move, through some kind of biological link, to a new brain, then it is possible that the same continuous consciousness could now exist in the new brain.
(to be clear, I don't mean any of what I said to be insulting. I'm just observing that there are perspectives on this issue that I don't quite understand)