Do Volly deFaut and Danny Polo count as Chicago clarinetists? If so, I think we'd agree they were closer to the Goodman rather than the Tesch mold, especially Polo.
It seems to me that Tesch "got" the Bix idea of playing "unusual" note choices and combinations but not the concept of making each note a "pretty" one, although he certainly put together some pretty notes a la Goodman at times.
I think both McPartland's and Tesch's solos on "Liza" show Bix's influence, for example. I also like the way Tesch plays high harmony note for note with McPartland's lead on that song, rather than the usual clarinet embroidery all around the melody. He does some of the same to good effect on "Shim-me-sha-wabble" with Red Nichols in the second half of the song. Tesch was usually surprising, certainly never boring, and probably best personifies the explosive energy of the Chicago style.
It is surprising that he made so few recordings, yet is far from forgotten. I can't help but wonder what Bix and Tesch might have done together later in a small group like Goodman's trios/quartets and Shaw's Gramercy Five.