No unfortunatley AKL does not have public computers. Only the convention hotels have them, they are located in their Convention Center buisness centers (Boardwalk, Contemporary, Coronado Springs, Grand Floridian and Yacht and Beach Club) these are avalaible to anyone (as stated they are $10 for 15 minutes or $40 per hour) if you really need one.
You will still have the High Speed access ($9.95 for a 24 hour period) and/or regular dial up access (75 cents per connection) if you have your own laptop and are able to bring it with you.