Won't work. The Beast's Chalkboard is simply a DC offset generator coupled with an adder, with the offset adjustable only in 1V steps. It doesn't accept audio as such, although there might still be some "abuse potential" there inasmuch as you'll be shifting audio, but at the same time you'll run into the issues associated with having DC in your audio path, which you DO NOT WANT because...well:
Now, what you REALLY want here if you want waveform mangling AND suboctaves...that would be something like Tiptop's Fold processor, which does both admirably. Split your E352's audio out for the "clean" line and the "dirty", then use the Fold on the latter. This gets even MORE fun because you have separate outputs for the wavefolder and octave divider (which ALSO offers levels per suboctave!), meaning you can have THREE potential outputs from the E352 with different "flavors". Oh, and the Fold will also take two inputs and "mix" them through its circuits, sometime with really amazing results. Useful thing, really.