It would have been on brand. Let me tell a story about a different musician.

Milt Hinton, jazz musician, and one of the great bass players of the 20th century, was delivering liquor for Al Capone. He was also black.

He got into an automobile accident and one of his fingers (needed for playing music) was injured. Al Capone went with Hinton to the hospital; the doctor wanted to amputate and leave off the finger, but Capone made a personal plea: the doctor sewed the finger on, and it ended up being good enough to play all through the 20th century.

Al Capone not only worked with blacks within his organization, but helped musicians through trouble and would provide bodyguards when needed. Entertainers and mobsters lived in a tight relationship (although as you'll see shortly, not a symmetrical one), simply because so many of the venues to perform in were run by criminals. This was not always optimal for musicianship. The cornet player Jimmy McPartland later wrote of performing at one of Capone's clubs:

All over the place people were gashed and bleeding. The mobster would break a bottle over some guy's head, then jab it in his face, then maybe kick him. They made mincemeat of people ... but we just kept playing -- period.

While it's certainly not true that all cabarets were mobster-run -- one early innovator, the famous boxer Jack Johnson, started the Cafe de Campion in 1912 as a "black and tan" (*) -- mobsters and nightclubs were tightly wound with the rise of Prohibition.

'Tis a sad, sad day for me

This day of lemonade and tea

For now my dancing aspirations haven't got a chance

In the Harlem cabarets

-- Irving Berlin, You Cannot Make Your Shimmy Shake On Tea

It meant many entertainers passed through mobster establishments if they were intending to make it big in Chicago. In addition to Waller, Duke Ellington, Ethel Morton, and Ethel Waters all performed in mob country. Again: treatment of performers was generally good, as long they didn't stray over the loyalty line (and if carnage was afoot, they kept performing).

The comedian and singer Joe Lewis is a good example. He performed at the Green Mill (a club of Machine Gun Jack McGurn, one of Capone's gang) but when his contract ended he went to a rival gang's club (the Rendezvous, run by the Moran gang).

McGurn threatened Lewis; not long after a successful performance at the Rendezvous, three men visited him in his hotel room, two with guns and one with a knife. After extended working over with the knife, Lewis landed six hours in a hospital. Part of his tongue was cut off.

The Fats Waller story about the birthday party is probably true. Maurice Waller, his son, later recounted in detail his father's narrative.

Fats had been performing piano at the Hotel Sherman:

Soon he began to notice a bunch of mugs in black ties and wide-lapeled suits coming to listen to him nightly, but thought nothing of it. Then, one night these gentlemen leaped up from their seats, pulled out machine guns, and told everyone to be as still as possible as they searched the audience for a ''friend." Satisfied that they had found their acquaintance, they told the rest of the audience, a rather large group of people, to get into the men's room. Dad was the first in and had to be persuaded to come out after the police had arrived.

On a different night, the same gentlemen in black ties showed up; when Fats was done with his gig he left relieved nothing had happened, but soon found himself forced into a limo at gunpoint.

He was worried, at the time, it had something to do with the first incident, but instead he arrived at -- as the story you mention goes -- at Al Capone's surprise party. He was "asked" to play piano but soon the environment became more relaxed:

In fact he swung it so hard, Capone kept him there several days, shoving hundred-dollar bills into his pocket whenever he played a request, and filling his glass with vintage champagne whenever Dad (frequently) emptied it. After the birthday party was over, three days later, the mugs returned him to Chicago several thousand dollars richer. Dad always said the incident stood out in his mind because it was the first time he ever drank champagne.

Now, I say "probably" to all this because another book -- this one by Al Capone's grandniece -- tells things a little differently; that Waller was one of the musicians who got his start through Capone's nightclubs, although she also mentions the stuffing of hundred-dollar bills. However, Fats Waller's career really did get going long before Al Capone came into the scene, and the behavior of the mobsters doing a kidnapping is really not out of character.

To return to the essential point: Al Capone really did seem to care for African-Americans, and it is unlikely in the midst of a multi-day party anyone would have been abusive to the guest against his wishes. This quote supposedly from Capone himself is second-hand as told to his brother, but fairly plausible based on Capone's other actions:

... these poor bastards are going through the same kind of crap that us Italians had to put up with a generation ago. Even worse! So I'm glad to help them make a living, especially when they are as talented as these guys are.

...

(*) Roughly, one where interracial mixing was allowed, although rules could vary.

Capone, D. M. (2010). Uncle Al Capone: The Untold Story from Inside His Family. Recaplodge LLC.

Iorizzo, L. J. (2003). Al Capone: a biography. Greenwood Publishing Group.

Ogren, K. J. (1992). The jazz revolution: Twenties America and the meaning of jazz. Oxford University Press.

Vincent, T. (1992). The Community That Gave Jazz to Chicago. Black Music Research Journal, 12(1), 43-55.

Waller, M., & Calabrese, A. (2017). Fats Waller. U of Minnesota Press.