Hi Darius,
Basically: Yes, you can do that. But it's pretty messy.
- You can (of course) press play while you're in the style creator and live-record that into the DAW. Just realize that the style loops so you'll probably have to remove some extra stuff at the end of your recording.
- You also do the reverse: press record in the style creator and 'play' what's in your DAW back into the style creator. But this is where the mess comes in. Since the style creator works track-by-track, you must do this track-by-track. The style creator only records from ch1 or ch2, so you must set the DAW to send the track you want to 'transfer' on that channel. This is a real pain as none of the sounds will match! Plus you have to do it 8 times for a full style part. More interestingly, when you originally recorded from the style creator into the DAW, the style creator sends all kinds of sysex at the beginning. Depending on your DAW, this could be very challenging to deal with. Then there's the matter of clocking: no matter what I try, I cannot get the style creator to 100% sync to the DAW.
Personally, I like creating my styles on the keyboard itself, since you can go back-and-forth quickly between actually playing your style and seeing how it deals with chord changes, and editing. However, the editing functionality in the style creator are pretty limited so it would be nice to SOMETIMES edit "on the big screen". In the end I found myself spending more time on figuring out how to properly transfer between DAW and Genos than actually making music, so I gave up.
You're better off creating the entire style in your DAW (that structure isn't too bad - a few bars for Intro1, a few for Intro2, a few for Intro3, then MainA, MainB, etc... You can easily find this on the internet), save it as a midi file and then use a utility to add the technical pieces that tell the keyboard how to play this as a style. It needs to know what kind of transposition rules to apply, what the high/low notes how, how to deal with chords that change while notes are sounding (think a pad/strings, for instance), etc. Mixmaster from Michael Bedesem is pretty good, but for ultimate control you'll really want to become familiar with Jørgen Sørensen's utilities. I haven't tried Stylemagic YA, but people seem to have good luck with that as well.
With Jørgen's utilities, you can basically take an existing style and split it into two pieces: the midi file and the technical stuff. You can then edit the midi file in your DAW, save it, and then merge the technical stuff back in to create a valid style file.
You can also just open a .sty file as a midi file in your DAW (just rename it to .mid if you have to). You'll loose all the technical stuff, but you can see the structure.
Hope this helps,
Peter