Yeah, that parking lot there is nice, and if you get there early, the street right before the parking lot (actually alongside) the parking lot, is free and right by the showerhead. It looks like you are right on the water, but there is that huge sand berm. I sometimes surf fish that spot for halibut, and it's not easy to climb up it with gear! I wondered how it would be to manage with a kayak.
Yesterday, I kayaked Mother's Beach, and helped a guy load his kayak. It was a sit-in ocean-style kayak, and he launched from Mother's, exited the jetty, and went all the way to the breakwater and back to Mother's Beach.
So.. I guess it's definitely do-able! Nice day to yak.. I wish I was out there.