2019 Season: Bus services from Matsumoto to Kamikochi are scheduled to begin on April 17, but not all facilities will be open then. (see here for details). The park will officially close on November 15. If you are thinking of entering the park in the winter, you should consult with a guide about possible activities.
No. The local buses and the Matsumoto Dentetsu train line is operated by a private company (Alpico), so the JR pass is valid only to Matsumoto or Takayama and does NOT cover the train and bus from there to Kamikochi. However, Alpico does offer a convenient 2-day or 4-day pass, which is a bargain if you also plan to visit the neighborhood.