No. By the time the Goodman band was established, Dorsey was already co-leading the Dorsey Brothers Orchestra with his brother Jimmy.

Tommy, Les Goodman, Charlie, Sally, Charlie's wife, Pete Van Horn, Goodman, Women One and Two, Steve Brand

Benny Goodman, Tommy Dorsey, Red Nichols, Gene Krupa Orchestra

There were many. Duke Ellington, Benny Goodman, Artie Shaw, Glenn Miller, and Jimmy and Tommy Dorsey.

Swing and Big Band Jazz was the POPular music of the day.. ( Benny Goodman, Tommy Dorsey, etc )