I've fished off a surfboard near the pier.
Ladyfish were running thick while I was surfing one day, had the rod in the Jeep and figured, what the hell.
Caught a few then lost the rig to a king. Didn't feel like going back, re-rigging and back out so left the rod on the beach and just surfed.
I carried it our in my teeth, no basket but that setup looks like it'd work really well -- try it in cobia/mako season!