No, Japan did not have a Christmas display of crucified Santas in a department store.

The Urban Legend: "During the years of the bubble economy in the 80s and 90s , when the Japanese economy was booming, a legend sprang up that some time after the war, in the 50s or just a few years ago a department store in Japan innocently put up Santa Claus on crosses, thinking that was appropriate for the season."
There are not a lot of Christians in Japan, but everybody there knows that crucifixion is a way of killing someone, not of honouring them - Christians were crucified in Japan in the 17th Century after the religion was outlawed, and POWs were crucified by the Japanese military during WWII.
There aren't any news articles that support the crucified Santa claim, but one image I keep seeing is this one by Japanese photographer Yoshio Itagaki of an apparent department store window display of a crucified Santa - http://www.yoshioitagaki.com/2008/ul/slideshow/santa.html - it's really part of a series he is doing on urban legends.  It's not a photograph of a real store in Japan. It's a work of art.

Snopes - Did a Japanese department store once display Santa Claus nailed to a cross?