Unfortunately, daisy-chaining sound cards like you are trying to do will only degrade audio quality. On a most basic level, sound cards convert digital signal from your computer (aka '0's and 1's') into analog voltage-based signal (waveform through changing the voltage running through the wire at a rapid pace).
Both your soundcard and your headset minibox are doing the same thing, so it would just be repetitive, and most likely quality degrading, to change your digital signal to an analog signal from your sound card, then back to a digital signal through an adapter, then back to analog for the headsets.
As for in the OS, changing your default sound driver would only make it so your USB headset would not receive information from the computer, it wouldn't make it so the soundcard would be doing any sort of pre-processing or anything.
I hope this has cleared up the confusion a bit. Basically, you will get better audio quality if you stick to the headphone processor.