The first thing that springs to mind for me is Avatar: The Last Airbender. It's like being able to call a past spirit and communicate to it for advice, although you can do it with real people as well and actually interact with them.
Using that as a basis, I can easily see this becoming highly utilized. Imagine the changes to schooling. You can simply get a temporary copy of your professor that you can interact with whenever you need assistance with a question. Or you can talk to an expert in any field without bothering their real self. They can also perform any basic tasks, assuming they have an actual avatar body to work with.
But it does present some large legal and ethical issues, depending on what status the uploads are given. These virtual people, since they effectively have real minds, need some kinds of protection or protocols to go with them. I assume that, since they're software and you already have protection against illegal uploaders, you should already have some layers of protection from them (like preventing virtual mental/emotional abuse).
Other potential problems:
- Torture for information: Ethics?
- Communication with dead relatives: Emotional problems?
- Lying uploads: The person is an... unfavorable person?
- These uploads are a snapshot of their mind, which can have various issues. When they are taken will have to be very regulated.
EDIT:
With the most recent edit (stating uploads can have physical bodies and be limited by the user on their interactions), it begs the question. Why not create a single person and upload a bunch of that person to robot avatars trained in combat, prevent them from talking to anyone, and send them on missions with as much information as needed? It's a super soldier that can have full information that can't be cracked, and they can make decisions with that full information in a way the creator agrees with. If they can have an physical interactions in actual reality, it presents huge military complications.
Overall this ability is almost too viably productive (for any means) to not be used. Even if these uploads are purely limited to a VR environment where people choose when they interact and how, it essentially equates to easily accessible labor.
The question should be less about IF a market will develop and more about how to regulate the market and what markets it will change.
EDIT 2:
Based upon a small conversation in the edits section.
There seems to be a common theme among answers: mass reproduction. The direct way to counter this is to have the uploads degrade in some way. Does uploading your mind or making a copy of the upload degrade the final product in any way?
I assumed that it would put the mind under significant stress to be completely replicated. Downloading a computer file that's 3 gigs takes long enough on a computer compared to a human brain putting up with the stress of copying anywhere from 10-100 terabytes. So multiple splits in succession cause damage, since the upload would be stressed as well. Too much stress results in decreased mental capabilities and symptoms like PTSD and anxiety, which can lead to that depression and suicidal tendencies.
This kind of degradation of the uploads could limit each person to uploading only once every few years. Even if each upload made a copy as well, this prevents the 1000-copy scenarios of specific individuals, which makes uploads of higher intelligence more valuable.
Example: If you're a scientist, make an upload of yourself that will do work for you while you study as much as possible. Once you can split again, do it, and sell the old version for money. If you can only split once per 2 years, in one decade, there can be, at max, 16 of that version of yourself, and 32 of yourself in total. It would take 20 years to make 1000 of yourself, and half of those would be very old versions. This makes new uploads have a much higher value.