Some quick searching makes me think it is unlikely, but technically possible. The AKC says that the breed originated back in the 10th century in Wales. The warring states period of Japan is the 15th and 16th century. However, corgis were primarily used for cattle herding at the time, so I don’t really think it likely they would have been imported and used in Japan.

They are very cute though, so it makes for a fun premise.