This absolutely happens. Fisher boats will turn off AIS routinely. The nonprofit Global Fishing Watch is doing research to analyse AIS signals, and determine if illegal fishing happens in protected areas. See http://globalfishingwatch.org/fishing-vessel-behavior/signal...

If you browse their site, there's also stories about other illegal activities, such as laundering fish (it's being mixed with fish caught in legal areas on sea). Also some boats are staffed with people that are essentially slaves. They typically stay on sea permanently, and are fueled on sea. (http://oceana.org/blog/how-global-fishing-watch-can-combat-s...)