All NCL ships have Wi-Fi. However since the ship is mostly metal, the Wi-Fi signal may not be the best at all places.
You can purchase minutes in blocks of 30/60/100/250 or pay as you use.
Remember that the ship uses satellite communication for internet connection and it's quite slow.
For more information, check out this link
Number One Contributor
Yes, but it's not free and since it is a satellite connection it is not high speed. Refer to the following link for more info and fees.
Top 10 Contributor