Is it possible for Audacity to be used as a live input stream, as in:
Input (Mic/Internal Sounds) → processing/effects (Audacity) → Output (a virtual output device that can be accessed)
One of the ways I would utilize this is real time static noise removal, to save having to go back and process the audio afterwards, it would do it in real time.
No, Audacity does not do real time processing.
You can do it with a real-time VST effect host then send the host output to Audacity to be recorded.
Depending on the host you may need to use a “virtual cables” solution (search for it) to give Audacity an input to record from.