I think you can accomplish your goal but not exactly as you've presented it here. Kent is correct that BIAB tracks will follow the tempo map of the BIAB project song. However, BIAB generated tracks follow that tempo map whether it is an accurate and steady beat per bar or if it varies per bar. So you will need a tempo map recorded as a live performance without following an exact click track.

I import a lot of prerecorded songs that were recorded without a click track and vary throughout the song, speeding up in areas and slowing. I create a tempo map that follows this 'live' recorded audio and then generate BIAB backing tracks that follow that tempo map and the generated tracks speed and slow along with the original music track.

As an experiment based on your post, I imported a raw audio track I have on hand of a gentleman playing guitar and singing a song out by his pool. The timing the song if fairly inaccurate drifting a bit throughout the song.

I opened his song in RealBand which has a feature to manually create a click track as the song plays. I created a click track and exported that audio. I'm not a drummer but in my opinion, it will be nearly impossible to follow just a click track that follows an erratic and varying tempo map. There's no cue to alert you of the variations.

What I think will work for your quartet that wants to have the sonic embellishments of studio recording available for live performance is to have one of the prerecorded instruments, Guitar or Keyboard play live throughout the live performance and the band follow the tempo of that instrument rather than a click track. The instrument that's recorded in the studio will have an average tempo, for example 122, that can be used to sync the band with the instrument and an 8 beat count in to the drummer will give the drummer a four count in ears/monitor for a 4 count live count in to the band.

I've done this with recordings many times in both directions, BiAB tracks for live playing and syncing live recordings with BIAB tracks but have never attempted it live on stage but see no reason it will not work. The key to successfully doing what you want is in creating a live recording that does not follow a click but is a natural, flowing performance. A BIAB generated rhythm guitar playing as a 'live' player throughout the song for the band to follow is a good example how to accomplish what you want to do. Think of the track as being a guest guitarist sitting in with the band at one of your shows. It's the same concept.

BIAB 2025:RB 2025, Latest builds: Dell Optiplex 7040 Desktop; Windows-10-64 bit, Intel Core i7-6700 3.4GHz CPU and 16 GB Ram Memory.