Live Pass Through, but with Effects being applied

I am thrilled that Audacity can invert the wave form. It means I might be able to do experiements in noise cancellation. However, I can’t seem to figure out if there is a pass through mode of the incoming signals while reading it and appling the effect invert to an outgoing channel

Only on Linux (using Jack) as far as I’m aware. Audacity does not currently do real time processing.
For “Invert” you can wire your loudspeakers the other way round (red to black / black to red).