Yes...there is an area right by the ramp where you can walk down river. And there is a place across from the ramp below the bridge you could fish. How well folks do there I do not know but I see them fishing all the time.
Not much problem in cooler weather, but the saltgrass flats that area are normally well populated with rattlesnakes (unless the wild hogs have eaten all of them!). Few miles west, still on FM616, Garcitas creek bridge area might be worth a try. Just speculating.