iMessage is supported. Please turn off the ''send as SMS'' option from Settings > Message.
However, you cannot send SMS with the Travel Data Only SIM card.

PLEASE NOTE THE FOLLOWING:

1. For our SIM card, it comes with a number starting with 020, which is NOT a proper Japanese number.
Therefore, you will not be able to make/receive calls or send/receive SMS, but you can use iMessage or Facetime since these applications only use the internet.
2. When you use iMessage or Facetime, the ID will usually be the number registered on your iPhone. 

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3. When you insert the SIM card into your iPhone, the phone will ask you if you would like to "change to" this number for your iPhone, please tap on NO.
By doing this, the iPhone will allow you to keep your original number for the use of iMessage or Facetime.
4. If you tap on YES, the phone will try to verify the 020 number, which will make you unable to use iMessage while using our Travel SIM card.