School could be based on....
Third Street Music School Settlement in the East Village in New York City. The school was stated in 1894 and although larger than the film's version, it is designed to give the joy of playing an instrument to working class children.
My wife took piano there in the 1950s. And in the film, one of the kids mentioned that the school was on third street, which might have been a nod that this is what it was based on.
The movie was corny as could be, but an absolute delight. And it's interesting to learn from previous comments that the talented children were the actual performers, something my wife and I were debating.