The movie "Transcendence" with Johnny Depp goes over this in a good amount of detail. But ultimately I believe it's what you personally consider a "soul" to be.
I don't think that scientifically it can be answered through "yes or no" study, experimenting, and conclusion. With respect to Alt and her methods, we see how she turns out. She even states, "As a Netrunner, I was able to survive." But clearly through discussion with Silverhand and V Alt clarifies that she has simply "maintained" her awareness of her state within the Net. In other words, she is capable of registering actions and decisions in a logical format similar to Google's Sicamor Quantum Computer or NASNet respectfully.
My take on the whole "digital psyche" discussion is that Arasaka has laid out the format towards "holocrons" from Star Wars. 99.999~% of the psyches uploaded won't retain their former selves (Jackie only used repetitive phrases) whereas with Sakuro Arasaka himself we do see something akin towards actual personality transference BUT we don't know the man's history enough to say for sure since his lines are but a few from what we personally witnessed. Even when he's responding to the board member at the meeting he repeats a quote that the two of them shared.
The only "system" that shows complete successful transference of the psyche is, If I'm correct, Altered Carbon. But IIRC the show doesn't go into specifics of how the discs actually work. The show just blanket messages it with "this is a thing that exists and that's what you accept"
Another close take is the flash-cloned AI's in Halo. However, the problem there is the "lifetime" of an AI construct with Rampancy. Even though the brain of the creator has been copied, the AI is still governed mostly by binary coding. Are feelings expressed at times? Yes. But are these authentic, or responding to the original brain's interpretation of a scenario similar to the presented one the AI has encountered and the 1/0 response that is deemed most appropriate used?
To bring this point to a close I would acknowledge that Alt has done some intense "fighting" with other constructs or programs beyond the Blackwall that her Netrunner skills have granted her the ability to better infer what decisions are beneficial to her coding similar to an anti-virus program running constant checks. And when a beneficial or neutral program is encountered, she bases her decisions on its compatibility for her success.
Sorry for the long post. Love the game and all it represents. Cried at each ending cause of how much I loved my character and how I based my actions on my actual needs or desires in life. And I'm not ashamed to admitthis.