Sort of. They get holidays, like anyone else (to Balmoral, a castle in Scotland, which is basically “the Hampton of the North”). But even on vacation, they can’t escape. They’re photographed walking dogs, pouring tea, or wearing rubber boots while looking deeply philosophical. There is no “privacy” setting for a royal.
They also have a duty to keep the family name good. That means no divorces that are too messy, no scandals that involve llamas, and no public arguments about who gets the last scone. It’s a lifetime of being on. Exhausting, right?