Not that I know of although I don't think anyone does it--maybe off of the bridges and the sides of the street.
I've seen some people fishing off the rocks by Club Med. Never noticed if they caught anything. I thought it might be fun to try.
Locals have been known to fish the lagoon at night... and occasionally attract the attention of other locals (crocs)... I've been told in the past that ANY fishing requires a permit, and I'm reasonably certain that the signs at the public beach access say you cant fish. In any event, I would be truly surprised if you could catch anything worth keeping that close to the shore...