The August 23rd issue of Jinja Shinpō had a short article about prayers for Olympic success at Fujisan Hongū Sengen Taisha. This is the main Sengen Jinja, where Mount Fuji is the goshintai. The jinja has a subsidiary sanctuary on top of Mount Fuji, and actually owns the upper part of the mountain. (A good example of property where the symbolic value greatly outweighs the monetary value.)
The article reported on Olympic athletes who had prayed at the jinja for success in the karate competition, and returned to the jinja to offer thanks after they won medals, including a gold.
The really interesting thing about the article is that they weren’t Japanese athletes — they were Spanish. The main athlete mentioned, together with a picture of her with the ema that she offered at the jinja, is Sandra Sánchez, who won gold in the women’s karate kata competition — after beating a Japanese woman in the final.
The Spanish team had been staying near the jinja, and so the priests had organised a prayer for victory for them. After her victory, she paid a visit to the jinja immediately before returning to Spain, to offer her thanks.
So, yes, you can pray at a jinja for victory over Japan — and after your prayer is granted, the priests will ask you back to offer thanks.
(Also, the photograph is small and I don’t really speak Spanish, but she appears to have written “Always with Jesus” on the ema. I suspect this would not have bothered the priests whether or not they were able to read it.)