I was chatting with their online agent, and asked this question since my wife is also planning on working remotely for part of the cruise. Here's what they said:
"At this time, we are not offering Premium WiFi on our Med sailings due to not being able to provide faster speeds in these areas. The premium WiFi is only offered during our Caribbean sailings."
"The unlimited WiFi is pretty strong, but we cannot guarantee it is strong enough to work remotely."