Icelandic ex-fisherman here:

Iceland‘s fisheries are controlled by what we call quota-kings. They are extremely rich owners of fishing quota (similar to USA’s oil barons) who are increasingly anti-social and obviously very unpopular among Iceland’s general public.

Iceland’s fishing system is kind of feudal in nature. People are allowed buy and trade and even rent fishing quotas. This means that the quota has accumulated into fewer and fewer hands of extremely rich individuals. The quota is then trickled down to fishing companies, and finally to fisherman, who have to spend a lot of money to rent the quota before they are allowed to fish.

This is a terrible system, and obviously the EU loves it (it even tried to copy it to solve the climate-crisis; and failed obviously). It fits smack into EUs neo-liberal trajectory. I don‘t think it is a fantasy at all the EU would adopt Iceland’s management policy at all. Nor do I think Iceland’s workers (including fishermen) have anything to worry about inside the EU. Trading ownership from our own feudal overlords to European bureaucrats would be a net positive in my books, however unlikely I find it.

That said I think it is unlikely Iceland will join anyway. Even if ‘yes’ wins. Iceland’s politicians have a history of ignoring the results of a national referendum if they don‘t like the results. They did this back in 2012 when the nation voted in favor of a new constitution (which relevantly would have actually transferred ownership of the fisheries to the Icelandic nation). A new government came to power and simply decided to ignore the results because their loved quota-kings would have lost power. I think something similar is likely to happen again.