Possible to purchase a 15 day pass?

Hi there, I will be arriving in Japan (NRT) on May 20th (20:30), but will be departing Japan (NRT) on June 3rd (17:00). I'm at dilemma right now as I'm not sure if I should take the Airport->Hotel Bus on arrival and then activate the JR Rail pass (14 day Green Car pass) the next day, or activate it upon arrival and then pay for Hotel->NRT Bus transfer upon departure. Does the JR Rail pass base their 14 day calculation on 336 hours of use upon activation, or if I activate the pass with only 3:30hrs left in the initial day, it counts the usage as a full day? Is it possible to buy 1 extra day?