I am aware that ebooks actually have a license (usually) which prohibits a user from sharing an ebook.
I am curious, if, as a programmer, I can have a system (say an online session) where only one user (not necessarily the original purchaser) can use/view an ebook (i.e. it is not replicated or distributed) at any given time, will it be legal for me to share my ebooks?
No, not as a general rule. Such a system already exists for libraries, where the library buys some number of licenses for viewing, where with 10 licenses, up to 10 people can check out the book for a period of time. If you purchase such a license, then subject to the security requirements (the rights-holder can demand certain security-type systems), you can let as many people read the book at a time as you have licenses. If you just buy a book on the ordinary market, that license probably does not allow "sharing". It really comes down to what license you have obtained.
You can't do this with Amazon Kindle content. This is from the UK Amazon Kindle license (emphasis and ellipses mine):
1. Kindle Content
Use of Kindle Content. [..] the Content Provider grants you a non-exclusive right to view, use, and display such Kindle Content an unlimited number of times, solely on the Kindle or a Reading Application or as otherwise permitted as part of the Service, [...] and solely for your personal, non-commercial use. [..]
Limitations. Unless specifically indicated otherwise, you may not sell, rent, lease, distribute, broadcast, sublicense, or otherwise assign any rights to the Kindle Content or any portion of it to any third party, and you may not remove or modify any proprietary notices or labels on the Kindle Content. In addition, you may not bypass, modify, defeat, or circumvent security features that protect the Kindle Content.
Unless you point a webcam at a Kindle and have robot fingers turn the pages you are going to have to break the copy protection on the e-books as part of your scheme.
Apart from downloading books you have purchased, transmitting Kindle content over the Internet in any form, even as a rendered image of a page, is a violation of the license. It also counts as making a copy of the contents.
Doing this at business scale would involve having lots of viewing sessions on lots of (presumably) virtual devices. This is also banned by the license.
Doing pretty much anything with a Kindle for commercial purposes is going to violate the license: even if you just rented out a physical Kindle full of e-books that would be a violation of the license.
