The pirate link to the West Country is strong and pre-dates the era of film though - Drake, Raleigh, Dampier, Teach are all from that area (yes, I'm mixing privateers in with pirates, since the difference is purely down to perspective). During that era Bristol was the second largest city in England and the main port.
In terms of culture, we have Pirates of Penzance by Gilbert and Sullivan also pre-dating the film era.

I'm not going to dispute the words being made up, except the "arr" which is just over exaggerated, but the accent isn't unreasonable by any means and probably accurate more often than not for English pirates.