I know nothing about stutter edit so forgive my ignorance, but maybe there is a solution in the environment?
If stutter edit only starts doing its mangling thing when you press a key, maybe the note on/note off data could also trigger a mute off/mute on on a bus set up to record in real time.
i.e. set up an aux send from the stutter edit track. Create a new channel set up to record from the send, and record arm the track.
Then unmute/mute the aux channel feeding the record track while its recording.
Nothing would record until you pressed a key, then the note on data would unmute the aux and the signal would flow through to the record track.
As I said, I know nothing about how stutter edit works, so I probably am totally up the wrong tree. But I figure the stutter edit output must be going somewhere in Logic, so you should be able to record it as it happens.
What do you think Rounik?