That's actually quite a good idea. Should be do-able.
I've discovered that there are in fact a whole range of 'remote presence' robots already available: The VGO ($6000), Double Robotics 'Double' ($2000+ipad), Beam 'Texai'($16000+support contract), Robodynamics 'TiLR' ($10000), QB Anybot ($10000).
The double is the only one that isn't seriously expensive. It's really a segway-style frame to clip an ipad to - which is a quite a smart way to do things.
All of them are hopelessly proprietary of course, so no chance of common interfaces to whatever bot happens to be available at a site. I wonder if a double could be reverse-engineered to be driven by kosher software.