Robert Cummings does not play an angel in this film. He plays the role of "Steve Martin", a songwriter who is instrumental in the development of Jolson's career. The angel character in the film is "The Angel", played by William Demarest.
The scene you're thinking of is where "The Angel" visits a young Al Jolson (played by Scotty Beckett), who is deathly ill with pneumonia. While "The Angel" comes to take him to heaven, the young Jolson's faith and love for life convince the angel to spare him.
It's easy to confuse this with another film, as the plotline of a young child facing death and an angelic figure trying to take them to heaven is a common trope in cinema.
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