Some clarification...
TXT/SMS messages are sent/received using the cellular network. By having data roaming or data completely off, you will be able to send/receive TXT/SMS messages.
iMessage or WhatsUp type applications send messages via the data network. These will not work if you have data roaming off.
WiFi on board, is sold by
DCL and this is only good for Data services such as iMessage or WhatsUp. This is NOT good for cellular phone calls or TXT/SMS.
Note that some services like iMessage will revert to TXT/SMS if it cannot establish a connection via it's data service. Since you will more than likely have data roaming off, if someone tries to send you a message, it will more than likely revert to TXT/SMS and will come in via the cell network.
While at sea, the company cellular-at-sea is the cellular carrier. They will charge via pre-negotiated agreements with your carrier. You should be aware that certain carriers charge for both send and receive.
For example, Verizon charges 5c per TXT message received. They charge 25c per TXT sent per recipient.
Many deals or alert type messages come via TXT. And unless you are in airplane mode, these will continue to come in. Further, most carriers will cache the messages for a few days. So if you turn off airplane mode for a quick call, all those cached messages will rush in.
There is NO WAY TO TURN OFF TXT ROAMING. If you allow cellular roaming, txt will also be allowed. Very different than data roaming, which you have control over.
BTW, while on the port, you are bound by the local cellular companies. You should check with your carrier for information about charges. These will vary depending on the country.
Hope this helps...