I think you can still enjoy the play, but it would help to have a passing understanding about the relationships between Harry, William, Kate, etc.
I don't care much for mob stories, but The Sopranos is one of my favorite TV shows ever. If a piece is well-acted and well-written (King Charles III scores on both counts) then I can personally find enjoyment from it even if the subject matter is not something I would usually get excited for.
Do you like Shakespeare's history plays? If so, then I would recommend this without any qualms.
Marie: Don't be in such a hurry about that pretty little chippy in Frisco.
Tony: Eh, she's a no chip!