When BIAB generates an accompaniment, are the parts generated independently, or are they generated in coordination with each other? For example, in generating a bass part, is the BIAB arranger function coordinating it with what the kick drum is doing, as a human arranger would do?

I would assume that the parts are generated independently, because human-style coordination would seem very complex even for a powerful program like BIAB.

If the parts are generated independently, then I could freely combine, say, a bass part that I liked (having frozen it) with any drum part that was generated on a separate pass using the same style, and this would be just as likely to sound good as if the parts had been created simultaneously. Am I correct?

The program is an intelligent song arranger. Mostly the parts are independent of each other. However, the choice of style, instrument selection and data on the melody or solo tracks can affect the song arrangement.

There is some observational evidence a melody or soloist part can influence parts selection.

PG Music selects which instrument parts initially populate a style. A style selects which sections of a midi pattern or RealTracks gets used. The programming is smart enough that if you select the same RealTracks twice both tracks will not select the same audio for playback at each bar. However, that is also dependent on how much original RealTrack audio is available.

When you regenerate a song, the program tries not to duplicate what was used before while still keeping within the constraints of the chord chart.

Again though, in my opinion the parts are mostly independent of each other.