Yes they can. The fresh coconut water is specially good (in moderation, no more than a third of their daily liquid intake). The fresh coconut flesh (skin) is good as well, again in moderate amounts. In the tropics around the world, coconut is part of the daily diet in some form. The canned/tinned stuff is OK as well.
You don't eat the coconut, Booga the shark does. You can feed him coconuts with the Coconut Cannon at Booga Bay. You need to find the three ingredients on the island (coconut milk, bone, and key ingredient) and bring them to the medicine man. Once you have a sleeping potion in a coconut, you can feed it to Booga with the cannon.