Just like everything else in the pirate sea, what you get from the chest simply depends on luck!
So it is possible to get the same pirate more than once.
Keep in mind, finding RARE and LEGENDARY pirates are much more difficult....
Don't worry though, whenever you receive the same pirate you ALSO get credits towards your My Pirates collection.
Once you fill the bar you are guaranteed to get a wild, new pirate to your collection! :)