Well, strictly speaking, emotion and what we tend to think of as "irrationality" is rather hard-wired into us and is a part of everyday decision making, so I would tend to think it would be more difficult to "clone" only the "logic portions" of the brain, without including the "emotional/irrational" parts, and still have a fully functioning "virtual human brain".

EDIT:

I think "immortal" is used here in the sense that you (or rather, your virtual "cousin") could never "die" of old age. It would be able to "live forever", given that it's not actively destroyed by an outside force.

There's no brain. What you're supposed to upload is information about brain structure. While information represents brain, there's no brain to dream. So you'll have to either make it or simulate it. Whether it will dream depends on whether ability to dream is completely defined by brain structure and nothing else. Also, I doubt it'll be possible to get this info without killing original in the process.

P.S. SMBC had a strip with similar theme.

All of this is assuming materialism to be true. It isn't.

Firstly, you cannot make a one-to-one match of mental activity to brain states. For example, the sensation of "tasting honey" is the same whether it comes from memory, imagination, or a mouth full of honey; the brain states are different. Since two events or properties cannot be the same unless the presence of one entails the presence of the other, a brain state cannot be a mental event, only correlated with one.

Secondly, materialism is even worse at dealing with intelligibles (entities that can be thought about) than with mental objects. The rejection of intelligibles involves the loss of the sciences. How can we say an argument is illogical, unless the laws of logic have an objective existence, rather than being states in the brains of those using them? How can one theory entail another if neither exists?

Um, I can tell the difference between a mouth full of honey and remembering/imagining a mouthful of honey, clearly it's not the same at all.