Really expensive (Score 1)

As someone who has spent time at sea on research ships and works with satellite communications on research ships for a living, I can say that it's really expensive once you get away from coastal waters. The US academic research fleet (UNOLS) didn't get full internet access until 2005 because of this, and even now it's very limited in terms of bandwidth compared to what you are used to in your mom's basement/dorm room.

Near coast, you can use your cell phone, but once you get more than 50 miles offshore, your options quickly become limited and really expensive. You are at the mercy of various satellite operators, all of which charge you a pretty penny for the privilege of using their birds. The fact that most satellites are positioned to concentrate on populated areas (read: land) makes satellite connectivity in the middle of the ocean a very pricey commodity. This is why they charge you on a per-byte basis - C-band internet connectivity is typically a couple of thousand dollars US a month for a whopping 256 kilobits per second of bandwidth.

With all of the nerdy stuff out of the way, the MV explorer looks like a really cush cruise ship rather than a research vessel so you probably won't get much of an "at sea" experience other than not being able to leave the ship between ports. Enjoy your active stabilization, swimming pool, and piano bar.

For others considering time at sea, the Sea Education Association is the real deal. I've been aboard the SSV Robert C Seamans, their Pacific-based ship, and was kinda jealous that I never got to do something like that while I was in college. The students get a chance to climb the rigging and really sail the ship, rather than just being chauffeured around on a giant floating school bus. Additionally, you get to do some real science on their ships. Port stops in Tahiti and the Marquesas are tough to beat as well.