They were a full band inasmuch as they were listed on the album credits as band members, but Fagen and Becker called the shots all the way down the line, set it up to be a core band with studio musician guests, and wrote all the songs by themselves. For example, Fagen and Becker didn't like the solos Skunk played on "Reelin' In The Years," and got Elliott Randall to do it. And I would bet dollars to donuts that the money split was not an even one. The other guys certainly didn't share in publishing, that's for sure.
Fun fact: Elliott Randall played that solo using an SVT and 810