Does a USB Headset require any Specific Soundcard?
Solution 1:
Short answer: Yes, it will work, but possibly with slightly lower quality than a dedicated sound card.
Long answer: Typically, USB speakers/headphones will use software acceleration, i.e. built-in Windows drivers. However, it is possible to have hardware acceleration, but I'm not sure if your sound card needs to explicitly allow it. In any case, since you're buying a cheap headset, sound quality isn't such a big problem, so software acceleration should be fine.
Solution 2:
USB Headsets are soundcards. Only 1/8" jack type headsets go through the onboard soundcard.
Source: regularly configuring PulseAudio on Linux.