In the Known World, we saw that large cities disappeared from the map, while small, but not the smallest, towns became the new "big cities." Japan would most likely see something similar. Upon further research, the mainland would almost certainly be completely infected, but I still think the other islands would have a pretty good chance. One of the reasons Japan imports so much food now is how densely populated it is. A lot of people are working in cities, and thus don't produce food, but the (to a varying degree)less urban smaller islands could potentially be sustainable. They are also much less frequented by tourists, and less likely to be infected.
On another note, there is evidence of survivors in the Faroes. They were shown on the world map, but as part of the Silent World. However, on page 196, there is a section specifically showing the portions of the language trees containing Nordic languages. It also shows many speakers there are in the year 90 relative to the number in the year 0. On the Faroese section, there is a light blue dot. This could be an accident, or it could mean the Faroes are inhabited, or it could mean there are some people in the Known World preserving the language. It's probably an accident, but hey, maybe not.