Not out of the question, but not recommended. A few intrepid souls have made the journey though. A few years back, I rode down the east coast and rode for a fair while with couple of gents who were on Ducati 1050 Multistradas. They rode them like dual sports though and as Cam mentioned, you'd have a better time on a trail bike or a true dual sport.
On the other side, a couple of years back I ran into a fearless Finn in Angola who had ridden his R1 down the west coast. It's upping the adventure quotient if that's what you are looking for, but really they are both dual sport routes, with the west having much less good roads than the east.