I assume the BFLabs ASIC is handling all of the processing for mining since pairing the CPU across USB would be a little silly.
Thus the PC host is just for network access, right?
If I use a low powered host PC (Atom), it should have no effect on mining speed. Is this correct?
That is probably true. If you do any mining on GPU or FPGA already, you'll see that CPU usage is extremely low. People use Raspberry Pis with BFLabs' current Singles with no problem, and that's about as slow as you can get as far as CPU power goes.