As @natehorn said, that switch is for your input source, not for the routing.
I have 9/10 set to PC on mine 99% of the time, and this is my main mix coming out of Ableton.
I have mics, synths and gtrs going into the inputs on my Model 12, and they automatically route into Ableton.
I go one step beyond this too, and remove my input sources from the Main Model 12 mix and route them directly into Ableton, add fx, then monitor them back through channel 9/10.
Works great.
You wouldn’t have any issues doing what you said you want to.