(Edit: they have done this for a region of interest: 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)
In South Africa, the Council for Scientific and Industrial Research (CSIR) has a solution called SeaFAR [0] that combines satellite-based AIS reception with low-resolution synthetic aperture radar satellite imagery to track ships with AIS turned off. The solution uses some machine learning approaches to not only classify (and if possible, recognise) ships from low-resolution SAR imagery, but to associate those with their tracks from before AIS was turned off.
I've seen the solution in use, it's surprisingly effective. I have no doubt there are similar approaches elsewhere, this is just one I'm familiar with.
[0] http://www.defenceweb.co.za/index.php?option=com_content&vie...