Ok, I know they wouldn't be legitimate, and I know only Henry FitzRoy was acknowledged, but what is the likelihood that he has unknown descendants out there?
If he had grandchildren, the chances are almost certain. Henry VIII lived 500 years ago, which allows for approximately 3 generations/century * 5 centuries = 15 generations, which can be... well I don't know the math but should be most people with any British heritage at least. To illustrate, check out this post on King John (and watch for estimates re King Edward III) , who lived 3 centuries earlier, and do be sure to follow the links downstream to the link to an /r/AskScience AMA
If Catherine Carey was, as is heavily suspected, the illegitimate daughter of Henry VIII and Mary Boleyn, then it's certain - Carey was an ancestor of Princess Diana, and therefore Prince William and his children.