In Ableton Live, the output of any VST instrument can be recorded onto an audio track. If you want to reuse the recorded audio, this is faster than using the File Menu's Render to Disk… option.
You can get your audio clips and MIDI notes to groove right by turning off the grid when writing funky sections.
Adding swing to clips is pretty easy in Live. Click the Global Groove Amount box in the top left beside the metronome button.