In an AVB network (a direct connection between two Series III mixers already is an AVB network), any mixer can use one of the "Stagebox Modes". One mixer has to be the FOH mixer and the clock of the network, while the other can be used in Monitor Mix Mode (no own Main mix) or Stand Alone Mix (Main mix and flex mixes completely independent from FOH). The network part in this configuration basically is that both mixer share their inputs and serve each other as stagebox. But with the 32 channel mixers this is limited to 32 input channels and 16 flex mixes.
When the mixer on stage is used in Stand Alone Mode, it will not pass Main L/R of the FOH console. You need to two XLR connections from FOH to stage (to the PA). There is no chance to route/patch L/R signals within the network.