Yes, just hit global record if working from the session view and whatever you do in session view is automatically placed in the arrangement view. From there you can render (bounce) each separate track, select tracks, and even the whole arrangement into whatever audio format you desire.
Rendering separate tracks is great, especially if you use another DAW for mix/mastering.
That sounds great because it doesn't seem like it's actually "recording" an audio file as you play, it's just writing all the track and automation information into arrangement view as you perform it in session view. This seems ideal for CPU performance.
In Mainstage there's no such luck :-(
Out of curiousity, I'm an advanced Logic user and I love it. But, I'm very interested in learning and using ableton for live use. Is that easy enough to do in your opinion (assuming I master Live's workflow as well)?
I began on logic, and love it as well. I learned a lot about the use of DAWs and all the fun little knobs and sliders that can create or change sounds. Knowing a good amount about logic made the transition to ableton super easy. I still use logic, but my main compositional tool is now Live.
I made the switch because live caters to my personal workflow and musical style. Since I work with quite a bit of loops, it made sense. I can arrange clips and sounds much quicker because things that are built and running can be looped indefinitely while I build other sounds and test them in the texture in real time. That was sort of difficult to do in logic, for me at least.
Other than that, Live is really great. I'm loving it. Definitely get the suite, though. The instruments you get are well worth the extra money. Corpus is great too. Glad I could help!