Well it can, and it's easy...
I can't speak for other DAW's but in Pro Tools, even as far back as PT8...when you import a BIAB track as AUDIO ( wav) such as Drums, which I do all the time......
That wav file is imported into your session as a single track which has a PT's session default of 120 BPM ( you can change the default when you create your session) The imported wav file will still play at whatever meter it was when it originated in BIAB. The DAW default session meter is now just a reference.
Over on the far left, on the track options field change the track from SAMPLES to TICKS. Pro Tools allows this to be done individually or globally so you change all the tracks at the same time from Samples to Ticks. Then should you need to change meter up or down, just do it at the BPM line on the transport. All tracks must be set to TICKS so if you do change the BPM in the transport window, the entire session changes meter , if they are NOT set to Ticks, only the ones set to TICKS will change meter, then you will have Jazz.
Remember, the BPM # in the transport window is now just a ref, the actual BPM is what your BIAB track is. BUT..you can change it by changing the BPM # in the transport window. SAMPLES to TICKS or it will not change the imported wav file.
I suspect this option is available in most if not all DAW's, it would be crazy for it not to be..
Process:
In BIAB convert all instrument tracks to WAV files. Stereo or mono. They will convert individually.
Point the individual track files to your working folder. I just use the BIAB Hard Drive location under BB/50 songs.
Create a folder on your recording PC called IMPORT files, just a suggestion. Move the BIAB wav files into that folder.
When creating a session in your DAW, IMPORT the BIAB converted tracks into your session as audio files. You may be able to grab them off the BIAB HD but some DAW's like to grab files from an independent location. So for me I use a new folder termed IMPORT files. Some DAWS want to see the imported files on the same drive as the projects.
IF BIAB is resident on your recording PC along with the DAW, this will not be an issue. Mine is not, BIAB lives on it's own Hard Drive and I run it from the HD so I can use it on different PC's.
Should a file come over in stereo, no big deal if you only want mono.
In Pro Tools you can split each track into MONO, then delete the one you do not want. I suspect most if not all DAWS do this.
This is a common process for me as I write many drum tracks in BIAB, convert them to wav then load them into a PT session. And yes, we change the session tempo more often than not .
easy as pie !