No, although Jimmy Giuffre was in the 4 tenor sax line up in a band in LA with Sims, Steward and Getz that gave Woody Herman the idea for a three tenor, one bari line up. Jimmy Giuffre composed the Four Brothers theme and arranged that and others for Herman but he didn't play in the band - or at least record with it - until Getz left, in '49 I think.
As well as the three tenor, one bari line up, the band had altoist Sam Marowitz as well, although he doesn't figure on the Four Brothers track or it's soloists As Woody Herman could play alto as well as clarinet it had a very flexible reed line up.