To record a single channel with the effect, you would need to record the main mix, one channel at a time. This will allow you to record exactly what you're hearing.
To take this one step further, ff you want to record all the channels with the effect of the StudioLive A12 (or AR8 / AR16)
Using studio one 3.3.2 or higher you don't have to create your setup manually. You can select a preset template. To do this create a ''new song'' then select the tab for ''interfaces'' and select the StudioLive AR12 Mixer Song Template and you are ready to go.