A quad or tri can definitely carry a fishing weight, leader and lure! The trick is to either build your own, or adapt a ready-to-fly with a servo to let go of the line when you want it to. A lot of cheap pre-builts allow you to turn the LEDs on and off. You many be able to adapt that to a servo instead, using a relay to kick when LEDs power up. Another thing to be wary of is that the downdraft of the props produces updraft too, so you'll want to fly the copter UP a ways to produce a low drape of line before flying away to the drop point. Don't want that line to get sucked up and tangled in the props!
The build I'm working on now will have a gross lift of around 10lbs! of course the quad will weigh that down by almost half. But if you're using more than 5lbs of line, you're going for the "bigguns". It may also be interesting to dangle a fish finder from a quad and have a telemetry radio send back the results. Then you can FIND the fish before dropping the line.
As hotneil points out, you don't want the quad to drop into the water. The boat idea may be better! But adapting a cheapo pre-built with enough range may be better to start than build a $1000+ quad and lose it. You may also find that you like being able to take "selfies" of your buddies and your boat from a distance, and most quads have cameras.
Wouldn't it be funny if you found you had more fun flying than fishing? I can see lots of opportunities for getting video of things from a boat -- especially inaccessible rocky areas of coastline, flying around rocks isolated by surf, or just capturing your boat or others from the air. I imagine wearing goggles and flying while standing on a rocking deck may be the best way on earth to get sea sick though.
