I think History Boys is a marvelous, though slightly flawed play. But I seriously doubt its success in America. The play is so distinctly British, what with the inside regional references, the college test preps and the entire system of English grammar school itself, im afraid this one may get a bit lost in translation, similar to woes expressed about Billy Elliot.
The article says that the entire National Theatre cast will reprise their roles. Given Equity's rules about foreign actors being able to appear in American productions, how is this going to work? Normally it's allowed only if an actor is deemed a "star" or is the only person who could possibly play the role.
I think this is possible because the broadway run is technically considered part of a tour. They are touring the show right now, and one of the stops, big as it may be, is Broadway. So I think it is a limmited run tour show, which allows its cast to remain intact.