As noted by many, the Canadians will come looking for you if you have an emergecny. They won't ask for a radio operator's license if they board you nor a ship station license.
If my MMSI comes into play for something other than a routine AIS transmission, there is an emergency on or with my boat. I want anyone listening in to have all the data that exists. IF the non-FCC MMSI number does not appear when transmitting a MAYDAY, hopefully you spent beyond the minimum for a radio and got one with built in GPS that transmits GPS location when you hit the "I'm going to die" red button on the radio. IF not, hopefully your chartplotter is still running and you can transmit your position coordinates without getting rattled as the water reaches your waist. If not, well, your hourly plot on the paper back-up chart will help. Trawlers are slugs so you won't be too far off and most likely will still be in sight of your "plotted" location if your emergency occurs in daylight hours. And if the Canadian Coast Guard cannot notify your next of kin, because they did not know your name and boat's name, your family will get the hint when you do not return home. Best of all, that did not cost anything.
The fee for the station license is about $200 but the license is for ten years, so $20 a year. Is that worth skimping on in an emergency? The restricted radio telephone license is free and for your life.