Not with this lady, the sculptor Vinnie Ream, although Sherman's biographer Michael Fellman claims they did have an affair in the 1870s. Fellman also reports a later relationship of William Tecumseh Sherman with the much less photographed Mary Audenried. That liaison was winding down in `1885 when The Last Circle of Ulysses Grant is set.
While it is not certain that Sherman (who was married) had these and other affairs, Fellman makes a good case for them. Sherman certainly had a very different character than his even more distinguished friend, the faithful husband and good family man Grant.
I had fun writing dialogue for Sherman, who was an energetic and controversial conversationalist, but structured his interactions with Mary Audenried from her point of view. The sex scenes' va-va-voom factor is perhaps limited by the ages of the protagonists -- he was 65, she 40 -- and the status of the relationship. Mrs. Audenried (the widow of an officer who had served on Sherman's staff), is in my version growing jaded and cynical about their long-running affair.