Did the pirates ever clash with European Imperialists?

Oh yes, and sometimes they cooperated. I don't know the specifics, but the Portuguese were allowed to settle on Macau after they had defeated the pirates that had made their lair there.

When the Dutch got to Chinese waters they had trouble breaking into the Chines market. In part because the Ming dynasty didn't really approve of foreigners visiting China, and in part because of Portuguese opposition (Portugal, was ruled by the king of Spain, who was also at war with the Netherlands). In an attempt to redirect the flow of trade towards their bases in Batavia or Taiwan, they tried to interdict the trade with Macau and Manilla, not just with their own ships, but also by encouraging Chinese pirates. One of these pirates, or privateers really, was Zheng Zhilong, who became immensely powerful. Calling him a pirate or privateer doesn't really do him justice, by 1627 he had 400 junks and tens of thousands of men under his command. He was more aquatic warlord than pirate. He was so powerful, and the Ming government so weak, that they decided to hire him, rather than fight him. Unfortunately for him, many of his followers turned against him after that. However, he managed to convince the Dutch governor of Taiwan that, just as the Portuguese had been rewarded, the Dutch might benefit from fighting pirates rather than helping them. This alliance worked beautifully in battle, but when the promised trade opportunities didn't transpire things turned sour. This wasn't really Zheng's fault, there was a new governor in town who hated both pirates and the (piratical) Dutch. Putmans, the Dutch governor of Taiwan, assembled a fleet of Dutch and Chinese vessels (he'd hired Chinese pirate ships by the hundreds) and burned Zhilong's fleet* at anchor in the bay of Xiamen, after that, he and his Chinese allies plundered their way along China's southern coast. The next year, Zhilong returned the favour and defeated the Dutch fleet, with the aid of fireships.

Oddly enough, trade between Taiwan and the mainland flourished after this. Zhilong got all the credit for defeating the barbarians, which allowed him to sideline the governor, giving him a free hand to allow, and profit from, trade with the Dutch.

Some decades later, in 1662, Zhilong's son, Chenggong (better known in the west as Koxinga), a Ming loyalist, would oust the Dutch from their main settlement on Taiwan.

Source: mostly Andrade's Lost Colony

AFAIK there were clashed between western navies and Chinese pirates throughout the 18th and 19th centuries as well, but i don't know nearly enough about it to post here. Hopefully someone else will weigh in on that.