The short answer is yes you can.

After you enter your chords you select a suitable music style and this style can be only RealTracks, only Midi or mixed. There are plenty of midi only styles available in the MegaPak edition and upwards.

If you are only interested in midi you probably don't need anything more than the MegaPak version which has more than 2000 midi styles.

You can export a midi file with separate tracks for each instrument from BIAB or use the BIAB plug for Ableton.

Regards
Tim