If you're wanting to use the SL24 III as the mixer outside of Logic then you need to firstly setup Logic so that each channel goes direct-out via the SL24 USB interface. You then need to set all channel input sources on the SL24 to USB.
Bear in mind though, with Logic receiving Mackie Control commands you'll be mixing twice. Logic will be responding to the control it receives from the mixer (faders will move etc) and then the mixer will also be affecting the audio. Not sure if that is what you had in mind?
So with Logic in MCU mode it suggests that you'd want to use Logic as the mixer and output a summed stereo signal. Probably easiest just to output via the SL24's Digital Return channel then bring that up in your Main Mix or Control Room output.
Alternatively you could use Logic as a 'tape machine' and just play multi-channel audio out via USB and mix on the mixer. Theoretically you could use Logic to record the MIDI from the mixer and store it as automtion data.