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IF you can find free WiFi, which is very rare in Japan you can iMessage if BOTH users have iPhones. iMessage is not texting so I don't think it applies to the question being asked.
True texting (SMS) is also very rare in Japan. In all my many times in Japan I've never used SMS mainly because no one I would text in Japan uses SMS. Everyone uses mobile email which used the data network.
I beleive SMS is possible depending on the carrier service you choose. My impressions is that it is very pricey. Check with the cellular provider you will use while in Japan.