I took a surf zone kayaking class and the one thing they told me that sort of stuck was that at some point in a sea kayak, you will broach. You will turn sideways to the wave.
Keeping a sea kayak headed straight in surfing a wave is very hard and is a special skill that needs to be learned. So is handling a broach.
I don't think that you will know if the rudder is useful in the surf until you actually learn more about surf zone kayaking.
That said, with the rudder down, it will hang below the bottom of the boat and might make it hard to brace into the oncoming wave. The rudder will keep the bottom of the boat in place in the water and the wave would be pushing the top of the boat and your body over. In the surf during a broach, you normally would lean into the oncoming wave and brace as it eh wave pushed you sideways.
Others with more surf expertise could describe this better and maybe have some first hand knowledge about how the rudder will act in surf situations.
I use a skeg now but when I had a ruddered boat, I used it to keep straight in the wind. Of course steering with the rudder down requires using the rudder since paddling strokes don't have much effect.
That thing about the rudder being out of the water might be true depending on conditions. Someone watching you might be able to tell you more.
P.S. That surf zone class was loads of fun and I learned a lot. I highly recommend it since a book or video can't watch you and tell you what you are doing wrong. I'm a self-taught roller but I don't think I would have managed getting past the initial learning curve without personal instruction.
The Kayak Wing
Reflective Hull Decals
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