It's possible!!!!- it's just not set up for abroad customers to register.
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If you put in your phone number + area code (+1) it should work just fine? :o
For the address, it has an "abroad" checkbox, but will not accept your zip. The zipcode is prefecture based, so if you don't have residency in Japan, you just won't have it.
...I'm not sure what anyone else did(?) so maybe I did this wrong, but i just put a string of 0's for it.*
You'll also need to enter your name in Japanese in order to register. I suggest looking up katakana of it if you don't know japanese/what it would be.
I hope this helps a little!! I'm sure there's better ways to do this & someone else might help more- but I didn't have any troubles.
*I also only suggest doing this for support/registration of products, since you won't be able to buy anything without proper infomation.