nvidia has some software that you can install if you have a compatible GPU which will take your webcam stream and blur your background or do other background effects. I suppose the challenge here would be to figure out which parts of the audio are the speaker's voice and which parts aren't, and remove the parts that aren't.

If the visualization of the audio is such that you can discern speech from other audio, similar to how you can discern the person's silhouette and figure out where the background is, then in theory it should be possible using the same technique.

I suppose there are probably some pure audio processing techniques that don't rely on the visualization as well.