Yes, as long as both versions of BIAB have the same styles, Realtracks, and other content.
And as you see in these screen shots, BIAB makes it easy and convenient to have the same styles, RealTracks and other content by identifying and assembling the necessary files to share between collaborators using an email specific for the task.
The command to access the special BIAB developed Email: - File | Save Special | Email Song File(s) as attachment(s)...