We were in Paradise Beach in January and I must admit, I didn't bring my laptop, blackberry, pda, cell phone or ipod. I did, however, have a great Margarita and swam a lot. I didn't notice any cell towers, wireless access points or wall jacks while I was there.
Check with one of the crew members before you lug you laptop to the beach. They know where all the wireless places are, especially the free ones. (The cruise lines don't even give them free web access as a benefit)
They don't advertise any free wireless on their website. You should email them from their site and ask. The guy that runs the place is really nice and uses his laptop at the bar. I don't know how he connects though.
Personally, I wouldn't even think of taking a laptop unless it was an absolute emergency.