I'm not sure about the musical (which I am obsessed with, by the way) but I'm almost POSITIVE that the Little Boy IS E.L. Doctorow (as someone mentioned earlier). Why you ask? I think there are many many moments that support my theory:
-he collects other people's trash
-the mirror chapter
-the ice skating chapter
-his "psychic" abilities
there are others, but I think all these character traits point to a person who will grow up to be a brilliant writer or intellectual of some sort :)
"Now she wants to know WHY, if I'm so fabulous, I would WANT to take care of her child.....I answer with as much filigree and insouciance as I can muster, trying to slightly cock my head like Snow White listening to the animals. She, in turn, is aiming for more of a Diane-Sawyer-pose, looking for answers which will confirm that I am not there to steal her husband, jewelry, friends, or child. In that order."
The Nanny Diaries