Instead of the Knights voluntarily splitting up for the search after the French taunting, like in the movie, the Knights run away and are scattered.
Arthur and Patsy find the Knights who say Ni, get their quest and Arthur gets depressed about finding a Shrubbery. Patsy then sings the song.
Yes, that scene is in the play. In fact, the whole Herbert thing is quite integral, as we learn that Lancelot is, as part of the song said, "Batting for the other team."