It has been done before, but not a non-stop ride. Wobbling Wally Watts did it! Apologies for the font tags- they changed the way the forum works. I’m having trouble viewing the pictures too but they are stashed in the unicyclist.com gallery somewhere.
An article on the net where I stole this photo says “between 1976 and 1978 he was credited with riding around the world, a journey of 12,000 miles.”