He can bring his laptop, but he won't be able to use it to dial into anything. I haven't tried to use the in-room phone to connect to my laptop and I haven't heard that anyone else has, but even if you could make a physical connection, the charges would be something like $7.95 a minute for every minute.
They do have an Internet Cafe on deck 3 aft with several computers available and they're connected to the Internet by Satellite. If you're on a 7 day cruise, you can buy the unlimited use package for about $89 for the entire week. You can also use it on a per minute basis, which is less than $7.95.
They have AOL installed on the pcs and you can also just go to the Internet using Internet Explorer. For Email, if you don't use AOL, you can use any web based email account to send and receive from. Some examples of web based email accounts that are free would be Hotmail.com and Yahoo.com. He should make sure he can use it long before he boards the ship so that any problems can be solved and he can be familiar with it.
They also have an Email account that you can use, based on your cabin number and their pre-established domain, but it costs a couple dollars per minute also.
If he has to perform work that is application based and only installed on his laptop, it will be very expensive to use. In fact, I don't know if the phones in the cabins are analog or digital, and that's important to know before you try to hook up your pc.
Hope that helps.