I'm not aware of anyone doing usability and experience research on a whiteboard outside of the industry, so I'd suggest asking your questions on Quora if you're looking for insider knowledge or access to research data. Based on my ~10 years of using whiteboards, I hope my personal experiences can be helpful to you...
One of the things that makes using any whiteboard an essential ingredient to my UX designs is uniformity of the experience across many different types and manufacturers of whiteboards and pens. While not all are created equal (I personally prefer anything that comes from EXPO to other brands since I've used many, many different surfaces and writing devices) I can recreate drawings within my acceptable tolerance for quality with very little learning curve based on the tool I am using. I know how to erase (with my finger, napkin, or felt eraser, and when to use which), which end of the pen writes, and how to hold it when it appears to dry-out, and when and where to spend $5 on new pens. Any learning curve added to this process for the device, reduces the effectiveness of the whiteboard to quickly convey ideas in a sketch. Since this cost is up-front for a project timeline, the financial and time investment in these tools is carefully considered. Any delays or changes are also frustrating so powering up an electronic screen or even waiting to start the software, where to stand when drawing, pens running out of batteries, etc. More importantly, if I'm going to go digital, I have a plethora of other things I can do in Balsamiq, such as including icons or images, grabbing standard shapes/containers or project assets I use repeatedly. This board quickly starts to look like Minority Report and has a massive learning curve and is no longer a whiteboard. Connecting my whiteboard to the internet, or even allowing me to save the state, for me, are not the most critical functions of the board. Understanding the user's need is the core of your product questions.
I think this question is truly about what User Experience and Interaction Design are all about - getting to the heart of what features you want to add to the current whiteboard experience and at what cost to the user base, financial cost of the tools, learning cost of adoption, and perceived or actual benefits of that system. Not just your product, but the entire ecosystem/infrastructure around how to get and use whiteboards. This research you are asking about, is in my opinion, product research you would need to assess if there is a market for your prototype, and how the experience you propose compares to a traditional whiteboard.
So the most credible answer I can give you, is as your end-user - the UX designer on many projects where at least 1 whiteboard (usually per room or person) is required to begin a decent project/startup. The board itself needs to be approximately the cost of a standard board aka priced competitively, available in enough sizes to fit in any office space configuration (I'm not choosing my office location based on which whiteboard will be installed, I chose the whiteboard that fits in the office I've chosen), and can accept any pen preference available on the market. If the board can then offer features like screen capture, simple wifi on my closed network for something like direct to dropbox support, or multi-casting to remote sites, I would start to consider increased cost of the whiteboard based on overall project needs and budget. So far no digital whiteboard on the market has convinced me to adopt.
Maybe somebody has a body of research you can apply, if not I hope this data point of one is beneficial.