Yes and No... Any of the 16 channel mixers (SL16, 16R) can add its input channels to the AVB network. The FOH mixer supplies inputs 1 to 16, the rack mixer inputs 17 to 32. You need to keep the three modes (Stagebox/Monitor Mixer/Stand Alone Mixer) in mind.

The SL16 can handle 16 flex mixes, but the console is physically limited to 10 aux outputs, which you can use inpendent from your network settings. As far as I know the 16R does not allow routing of outputs, which means that aux outputs 1 to 6 have exactly the same signal as the SL16 console. This means that auxes 1 to 10 are available at the SL16 and auxes 1 to 6 at the 16R. The 16R is the only mixer in the Series III range, which by construction is limited to 16 input channels, 6 auxes and 2 FX.

You better get a 32R...