Could my friend play either Dr. John Seward, or Quincey Morris, when he knows one is American, the other Brit?

Depends on the tone of the play... if you're doing it all old-fashioned and true to the book then it makes sense he doesn't play the part... It's like hiring a black girl to play the geisha in Memoirs of a Geisha... it's ridiculous... if it's modern then yeah... like the black actor that played Mercutio in Romeo and Juliet in the 1990s movie...