No, it won't be valid in Ireland, so don't waste your money. You won't actually have ANY warranty in Ireland on a watch purchased in Japan, if you don't live and will use the watch in Japan. Buy your watch in the country you live and will use it. This is especially important for Apple Watches which are cellular. Cellular bands vary around the globe and there is no guarantee a watch purchased in Japan will connect to cellular bands in Ireland.
Finally, Apple doesn't accept international shipment. If you buy the watch in Japan and live in Ireland, if something goes wrong with the watch, you cannot ship it to Apple in Japan. You'd have to get on a plane and take to Japan yourself.
Any savings you may see from buying in a different country can not only evaporate, but diminish into the negatives, when you buy an device like iPhone or Apple Watch in a different country.