They would not - there is no documentation for it, and life vests and other life saving gear in relation to it (like the life boat) were all 19th-century inventions, long after the pirates of the Golden Age of Piracy of the late seventeenth and early eighteenth century.

Depends on which pirates you are focusing on. If, like u/davidAOP said, you are looking at the Golden Age of Piracy, it will be a no. However, is you expand the definition to other sea-faring robbers known as 'pirates' through time, you might find some. River piracy was booming along the Ohio and Mississippi Rivers during the 18th to the mid 19th centuries and piracy on the Great Lakes went even into the 20th century!

According to this article, in the late 18th/early 19th century, Norwegians were using cork stuffed vests as life preservers. In 1852, the US navy required ships to carry life preservers.

However, while life preservers and American pirates existed in the same period, there are no first hand accounts of pirates actually using them. One might presume the overly cautious might have, but absolution needs evidence.