It sure can be done and is being done, but vast majority of kayaks you run into at open waters in La Jolla are longer. There will be days when the wind, swell and the current will make you wish your yak is longer a couple of feet to help you better plow your way through.
Just guessing - that outrigger will likely make your kayak more stable, but it would probably further slow it down. I would worry about my lines getting tangled in that thing... especially in situation when you bring a big fish on the surface... though good problem to have
Good luck and welcome to BWE!