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The answer is basically no or at least not on any remotely significant scale. It may seem strange that piracy was eradicated so quickly and completely after the surge of so many flamboyant and iconic Anglo-American pirates in the late 1710s and early 1720s, but the truth is that after the end of Queen Anne's War and the Spanish War of Succession in 1713/1714 there was a very fierce and concerted effort by all European nations and especially Britain to hunt down and destroy the remaining pirates that had so long disrupted peaceful relations between them and their trading partners. The pirates just couldn't stand up to it. But this didn't just happen in a vacuum either and it's important to understand the background and context.

Even decades earlier, piracy and buccaneering had already been on the decline in the Caribbean since at least the 1680s and even more so by the 1690s when the Caribbean became too dangerous for most pirates and the few who hadn't already accepted royal pardons (often to violently suppress their former buccaneer allies) and limited themselves to only "legitimate" privateering during times of war were forced to flee to the Indian Ocean to prey on mostly Arab and Indian shipping. The most famous example of this was Henry Avery who created a huge scandal when he attacked and captured the treasure ship of the Mughal fleet in 1695, seriously endangering England's trading relations with India and in the aftermath the East India Company promised to pay massive reparations to appease the Mughals and Parliament declared pirates to be "Hostis humani generis," meaning enemies of mankind, and vowed to eradicate them. Although Henry Avery managed to escape capture and disappear with his loot, some of his crew were not so lucky and in the coming years more who dared to turn pirate were captured and hung for the same crimes, such as William Kidd in 1701. However, by that time there were very few pirates actually left and William Kidd himself had originally been sent out on an expedition to hunt down pirates before engaging in some acts of piracy himself (ironically because after spending over two years searching for pirates in the Indian Ocean he failed to encounter any and his crew was desperate for pay) for which he was then tried and executed when he returned to New England despite apparently believing he could escape punishment due to political influence.

Then in 1702 something happened that set in motion both the launching of a new generation of pirates and the final end of the so-called Golden Age of Piracy. This was of course the War of Spanish Succession and the American theater of that war called Queen Anne's War, during which time the navies of France and Spain and especially England (Britain after 1707) were greatly expanded and lawful privateering commissions were once again granted, authorizing ships to attack enemy shipping. There were several large and successful (and lawful) privateering expeditions into the Pacific in 1703-1707 and 1708-1711 to plunder the Spanish, principally under the command of Woodes Rogers who would later be instrumental in suppressing pirates. Also serving in this war were many who would later become pirates, such as Edward Teach (known as Blackbeard) who apparently distinguished himself during this war. However, after the war ended and peace was officially declared in September 1714, the European navies that had massively expanded during the war were quickly disbanded leaving many former sailors and privateers either out of work or having to work for very low wages as merchantmen, which needless to say they didn't like very much. During the war the island of New Providence in the Bahamas holding the town of Nassau had become a hotbed and base for many privateers serving in Queen Anne's War and in July 1715 when the Spanish treasure fleet was wrecked on the coast of Florida by a massive hurricane, many of these former privateers sought to engage in "salvage" operations but quickly came into conflict with the Spanish who accused them of piracy and appealed to British authorities.

From mid 1715 to mid 1718 the pirates operating out of Nassau went from stealing from the wrecked treasure fleets to outright piracy against even British shipping as authorities increasingly cracked down on them and they saw there was no longer any point in exclusively attacking the Spanish. It was at this time that the first use of the "Jolly Roger" or skull and crossbones flag came about. Before this time pirates had always at least pretended to represent some legitimate national authority as justification for their piracy no matter how bogus, but after this point when they saw that all nations were utterly determined to eradicate them and considered them hostis humani generis they gave up on all that and flew the skull and crossbones (or sometimes a skeleton with an hourglass and bleeding heart, etc.) as a symbol that they were really at war against everyone and having the obvious meaning "surrender or die." Since Nassau was the main base of this new wave of piracy, the British government sent Woodes Rogers with a proclamation granting a royal pardon to all the pirates on Nassau and elsewhere who surrendered -- but to those who didn't they would be granted no quarter.

Henry Jennings who had been very active in plundering the wrecked Spanish treasure fleets took this opportunity to surrender along with hundreds of others, many also becoming pirate hunters such as Benjamin Hornigold. But some were die-hards and wouldn't surrender and others took the pardon but then quickly turned again to piracy. Woodes Rogers attacked and captured Nassau in July 1718 and the pirates that wouldn't accept the royal pardon fled elsewhere, such as Charles Vane and Edward England. Blackbeard was killed by pirate hunters in a battle off North Carolina in November 1718, Vane was shipwrecked in February 1719 before being captured and executed in March 1721 and Calico Jack Rackham along with the two female pirates Anne Bonney and Mary Read were captured by pirate hunters and executed in November 1720 in the Bahamas after initially taking the royal pardon but returning again to piracy.

The pirate Edward England who had fled to the Atlantic and west coast of Africa in 1718 (much like an earlier generation of pirates had in the 1690s when there were major crackdowns on piracy in the Caribbean) was more successful but he was marooned by his crew in the Indian Ocean in 1721. His most powerful successor Bartholomew Roberts was killed by pirate hunters in a battle off the coast of West Africa in February 1722.

A few pirates still remained in the Caribbean at this point but Thomas Anstis' was murdered by his crew in April 1723 who then surrendered to Dutch authorities in exchange for a pardon. The particularly brutal pirate Edward Low's crew was defeated in June 1723 off the coast of New England, and although Low managed to escape he probably died sometime the next year in the Caribbean. Another of Low's compatriots George Lowther was probably killed around 1723, and another one, Francis Spriggs, disappeared in the Caribbean sometime around 1725 or 1726. In Scotland the pirate John Gow led a mutiny and briefly terrorized the coast from 1724 until he was shipwrecked and then captured and executed in June 1725. In April 1724 the pirate John Phillips was killed off Nova Scotia in a "mutiny" by several men he had tried to force to join his crew, since by that point he only had 11 men left under his command. One of the very last pirates of this era was William Fly and his crew who were captured off North Carolina by pirate hunters after a piratical career lasting just two months and hanged in July 1726. After that there basically weren't any European pirates left.