> So, if I plug same source inverted and non-inverted into A-172, I get
> positive and negative full wave rectifier then

Yes.

> Would this work precisely with audio signals too

It will work even with audio signals but there are diodes in the A-172 that
cause a small offset voltage (the so-called forward voltage of each diode).
If you replace all diodes by Schottky types the offset will be a bit smaller
but not zero.

If you need a precision rectifier: there is one in the envelope follower
circuit of the A-119 (no diode offset). If you remove the capacitor (C6)
that is used to smooth the envelope output you obtain a precision fullwave
rectifier. If you add a switch that turns C6 on/off you could switch between
envelope and rectifier.

> A newbie question: How do I connect to GND

The simplest methode: plug a cable "half" into an unused socket. This will
connect the tip of the cable to GND.

Best wishes
Dieter Doepfer