Yes!
I started going down the path of building a ripple carry adder already (which seems to work fine). Then I was going to try for a full on ALU, then some sort of ISA that sits on top of it all.
I have no idea what the end result will look like if it all comes together. Hopefully I'll find some weird primitives along the way. :D
It's very hand-wavy, but I'm kinda hoping I can somehow have a machine manually constructed out of neurons that can naturally interact with one built with looser hebbian learning rules.
The ISA could be really cool, having lots of "combo" commands that might reduce program length dramatically. Think ADD and MULT and SHIFT all in one command, to give a simple analogy.
On the interaction, one system uses a clock signal / metronome and the other is all cascades. The clock signal is like a metronome calibrated to the duration of the longest cascade = "critical path." It seems clear that these can interact smoothly, as one simply has the training wheels of the clock, while the other is about progression-via-propagation.