A:Answer Is your mic linked to a console? If so, sorta, but depending on the console (PS4 or Xbox) you'll need to send your "party chat" through the external source (i.e. tv/speakers) as well as headset.
If your headset is linked to a PC, yes. There are several options here, and it is actually pretty customizable and easy to use. I personally use Streamlabs OBS for streaming to twitch, etc, and the Xbox Game Bar for xbox party chat, or discord for PC players etc. (I am not sure of an alternative for playstation). Using Streamlabs' mixer or another audio mixer (vbaudio, voicemeter) I am able to mix and stream different audio channels. If I didn't want the chat of the people I'm in a party with going through the stream, I can cancel that output to the stream, but still hear it on my headset, etc.