Very doable. People were doing this well befor float tubes and fishing kayaks ever hit the scene. I have a buddy down in Del Mar that goes out often on a long board so I would think that a SUP would even be easier. There is a tournamnet that I have seen that is ONLY open to paddle and long boards.

Use cheap gear as it WILL get wet. My buddy uses an old bass combo for bass & halibut and trys to keep it dry on the way out. You can wrap the reel in plastic and strp to the dect when paddling.

Go for it and post some photos. Try gooling this and you will likly get a lot of ideas.