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...)
(Having worked with people involved in EO and law before, I know it's not just fishing boats where AIS being switched off in certain places may or may not be evidence of other stuff happening)
(Having worked with people involved in EO and law before, I know it's not just fishing boats where AIS being switched off in certain places may or may not be evidence of other stuff happening)