I spent a long time thinking about this, but no matter how generous I am with the question, I can't come up with anything other than "no".

Even if we broaden the category of pirate to include groups like the Barbary Corsairs, we can't really really point to any advancements in terms of shipbuilding, cartography, or botany, at least not any that were recorded.

However, if we let our definitions get even grayer, people who might be pirates depending on who you ask -- like Sir Francis Drake and William Dampier -- contributed meaningfully to the exploration of the world with their circumnavigations, and the boucaniers of the Caribbean helped to settle and, in a mostly informal sense, map islands like Hispanola and Jamaica.

I am much less familiar with non-Anglo pirates, so it's possible I'm missing something, but I can't really come up with any other answer to this.

That doesn't really address your question in full, but the lack of answers was bugging me, so I hope this is helpful.

I have a book called History of American Sailing Ships by Howard I. Chapelle that is supposed to be a classic. He makes no mention of pirate ships except in reference to the navy ships designed to catch them.

However, he does talk about slave ships. Slaving was illegal after 1807 or so, so one could argue that the slave trade was technically a form of piracy. Plus they were profitable, so big shipyards in Baltimore and the like would build them.

Slavers had to be fast to outrun the Navy ships that tried to catch them. As he dryly explains:

The necessity of speed in a slaver was obvious, once the cruisers became active. There was also the very high mortality among the slaves from over-crowding during a long voyage, and so speed and profits went hand in hand.

He writes:

The slaver gave designers much information on the models of fast vessels, and undoubtedly had some influence on later craft, particularly fore-and-afters. It would not be hard to trace the effect of the slaver on the early schooner-yachts, for the pilot-schooners of New York and Boston in the 1840's were on the same general model as the slaver, and from the pilot-boat the best models of early schooner-yachts were copied. The interest in fast-sailing schooners and brigs in the United States during the 1830's and 40's ran high, and accounts for the rapid spread of the Baltimore Clipper influence along the coast. When it is realized that the slaver-schooners and brigs reached a speed of 14 knots in many instances, the high degree of development in their design can be appreciated. This is why the type appeared in other trades, particularly the illegal ones requiring fast craft. It was perhaps fortunate for American designers that there were so many illegal trades being carried on during the years between 1815 and 1845, for it is possible that the fast models of the privateer type would otherwise have been quickly forgotten. The fad for fast vessels, that came from the interest in the slaver and pilot-boat type rather than solely from trade requirements, had much influence on the development of the big clipper-ships of the late '40's and early '50's. The fad also accounts for much of the interest that led to the building of the yacht America, and it is interesting, while early schooner-yachts are being mentioned, to find that an American-built slaver, the Theresa Secunda (said to have been built in Philadelphia), became a British yacht under the name of Xarifa.

It has been a popular idea that the Baltimore Clipper, as exemplified by the slaver, disappeared with the coming of the clipper-ships; the fact is, however, that the old model merely changed names, becoming the pilot-boat type of early American yachts, the "sharpshooter" type of Gloucester fishermen and the basic model of every fast keel schooner for another fifty years.