This is my first time posting on /r/askhistorians, so ¯\_(ツ)_/¯ hopefully it's acceptable. Best source I have is this handy book—Piracy: The Complete History, by Angus Konstam—which really runs the gamut in terms of its coverage of piracy.
The first and most notable example of the "pirate dialect" that we all know and love comes from this guy: Robert Newton, who played Long John Silver in the 1950 Treasure Island movie. It's not certain exactly what caused him to be accepted for the role (i.e did the director already have a preconceived idea of how a pirate 'should' sound), but there is the suggestion that the West Country accent did not stumble into piracy by accident: there's been a strong maritime tradition in the region, and some of the most famous British pirates and privateers came from here, including Sir Francis Drake, who hailed from a town in Devon. The fact that he lived some four hundred years ago appears to be something of a non-issue in terms of the accent, as the West Country dialect has remained remarkably unchanged apparently since the Anglo-Saxons and Old English. However, due to just the sheer length of time, it could be argued that this is coincidental. Regardless, after Robert Newton's first appearance as a pirate, his accent did indeed become ubiquitous as the language of pirates even to this day (well, most pirates). Before him, there were three English language Treasure Island movies, two of which were silent (1918 and 1920), and the third of which (1934) starred an American in the role of Long John Silver.
So, in summary, it might have been representative of some pirate and privateer accents over the course of history—of course, given how basically every country in the world with access to the sea has had pirates, it is not going to represent every pirate, nor every time period of pirates—but this is not entirely certain. What is known, is that Disney hired Robert Brown to create what has become the most popular interpretation of a pirate ever, and he happened to hail from a part of England which has produced a large number of sailors over the centuries.
Hi, not discouraging other contributions, but while you're waiting, you can get started on this question in AMA - Piracy from Antiquity to the Present. by /u/Benerson
For more information on how English pirates may have spoken, /u/elphinstone1842 answers in What were the speech patterns for 17th century sailors, pirates, and buccaneers?