Of course he does.
Prince Harry has spoken about his new baby nephew for the first time since the birth of Prince George.
“When I saw him he was crying his eyes out like all babies do, I suppose. It’s fantastic to have another addition to the family. I only hope my brother knows how expensive my baby-sitting charges are. [My role as an uncle is] to make sure he has a good upbringing, to keep him out of harm’s way, and make sure he has fun. The rest of it I leave to the parents.”
Cut to the year 2028. Las Vegas. Prince Harry and Prince George wake up dazed, with a slight headache. They quickly realize they're in possession of a tiger and a baby.
Wait. That's the story of the Hangover, but it illustrates my point: Prince Harry will likely rewrite the book on being a "fun" uncle.