Yes, one can definitely do street photography at the beach. Here is a demonstration by Pelayo Gonzalez from Gijon, Spain with a picture taken in February.
This is what Pelayo wrote about his shot :
I was walking by the beach when realised about the cool framing shadows were projecting on the sand surrounding the surfer. I guess his location was not random. He was warming up so probably he chose the place where sun was still shining. I specially like the moment of concentration and the loneliness of the man.
To discover more pictures by Pelayo, visit these links :