No. You can use the same microphone and headset/headphones. Barring hardware incompatibility, one physical microphone can be muted or unmuted as necessary. Which means that you can unmute it in both the main RSI event and the InterStar ICP platform, muted in both, or muted in only 1 of them as needed.
Your headset will receive audio both from the RSI event and from InterStar ICP as needed.
You also do not need to use 2 different devices unless you want to.