When I boarded the ship when I still had my H1B visa, they only checked my passport for identification. When I mentioned that I had an I-94 card stamped with my visa information the Carnival employee didn't care at all. The only one who was concerned about my immigration status was Immigration and not until the end of the cruise. That official understood that as long as my travel visa was okay, he wasn't worried about the date on the I-94.
The previous poster had a lot more current information about the process, and I suggest you follow his advice regarding contacting the officials at the port you are leaving from... it has been almost 10 years since I went on a cruise with a visa, so while I think you're safe enough, things have changed since Sept 2001, so it might be smart to check with them. I'd hate to give you outdated information, although it sounds like he had no issues, because he checked in advance.