The amplifier of the speakers are usually built into the subwoofer. Seeing as there is a different sub for each model in a range (the 2.1, the 5.1, the 7.1, whatever) each with different outputs, you can't just plug extra speakers into the sub.
However, your idea for adding another 2.1/2.0 system would work. The downside would be that you wouldn't have nearly as much bass (due to lack of a sub) for the rear speakers.
Sound cards expect you to buy speakers in packages, and you won't get nearly as good a sound unless you use one.
You think it will matter? Those speakers have lowpass set realy high. ~120hz - 200hz on most pc speakers. Since the sats rely on the subwoofer for some of the midrange, it will be hard to tell if that channel is coming through or not?
Aster, before you drop another $120 on those speakers, consider selling the ones you have and buy some 5.1's to get your desired effect.