I've received some good leads on the question of what female blues singer Milhaud might have seen in January or February of 1922, despite the fact that I got the venue wrong: it wasn't the Capitol Theatre but the Capitol Palace, the after-hours place where Duke Ellington first heard Willie the Lion. According to Bill Egan, Mamie Smith is a possibility; so too is Lucille Hegamin. To my ears, Smith is a better fit for Milhaud's description than the more mellifluous Hegamin. Both women can be heard at the amazing Red Hot Jazz site. Bill Egan has a wonderful site devoted to Florence Mills, whom I recently mentioned in connection with William Grant Still's Levee Land.
Update: It's been pointed out to me that the date in Milhaud's memoir is wrong, and that he was actually here in January and February of 1923. Oh, this slippery Milhaud!
Yet more: According to passenger-liner announcements in the New York Times, M. arrived on the Rochambeau on January 3 and departed on the same vessel on Feb. 15. Mamie Smith was still in town as of Jan. 9, recording "You've Got To See Mama Every Night (Or You Can't See Mama At All)." As Bill Egan informs me, she went to San Francisco later that month.