Is there a way to record MIDI 2 Guitar output directly on the standalone app, without a DAW interface?
Or is there a way to listen to MIDI 2 Guitar audio without the DAW? Say I perform and have only the MIDI 2 Guitar app on.
I have listened to the guitar output both on the standalone app and with Ableton, and I get a feel the MIDI output is cleaner on the standalone app?
You can use MG standalone without any DAW. It will play audio and host synths on its own. But in order to record, you need some kind of recorder. MG3 will include recording features 
The tracking performance in MG is identical, regardless of whether you run Standalone or in a DAW, if you use the same samplerate and buffersize. However, some DAWs may process plugins in separate processes and it will cause one buffersize of latency.