http://www.via-alpina.org/en/page/771/questions-answers#Is_the_Via_Alpina_accessible_by_mountain_bike_ "The Via Alpina has been designed for the enjoyment of the walker. Therefore, many parts are not adapted to MTB and on some bikes are even prohibited. When Pietro Marescotti completed his tour of the 5 Via Alpina trails with his MTB, he had been able to cycle for about one third of the way, had to push his bike for another third and carry it for the remainder. He enjoyed his trip immensely but this is not something we can recommend as a designated MTB route.
However, there are plenty of tracks along and around the Via Alpina for the enjoyment of the mountain bikers. Enquire with tourist offices and specialist associations, who will be able to make recommendations, and please always be considerate for other users of the trails.
Maybe one day there will be a Via Alpina for wheels, but that won’t be ready in the immediate future..."
Nice find dgjessee, sounds like a good idea to stick around the route though