No - rather there is no change in consciousness but if you do the upload in one jump, your subjective self sees the discontinuity and mistakenly thinks there was a change in consciousness. You have to do the process gradually to trick it out of its error.
These are tiny, atomic, piecemeal changes that happen slowly over time.
If one of your neurons randomly dies right this instant, you would probably not subjectively notice, even though that neuron composes your subjective consciousness. Your neural network is highly redundant and fault-tolerant.
Yes, neurons in our brains are dying every day, but it doesn't affect our subjective consciousness. Are you simply saying that uploading, if it were done carefully, would not make any more difference to our subjective consciousness than neurons dying every day?
You wouldn't notice because "you" would no longer exist, by hypothesis. But I would expect that there would also be a huge objective difference in your behavior, easily noticeable by others. The "self-awareness part of your brain" is not disconnected from the rest of your brain and body; if it dies, the rest of your brain and body is going to be drastically affected.
In other words, your subjective consciousness is somehow changed but you can't subjectively tell? What does that even mean?