Ardour can natively record to BWF files. If you do not choose this option, then there is no timestamp in the audio files because by definition there is no accepted standard chunk to store it in. You would have to infer the timestamp from REGION positions, which may or may not be trivial based on the structure of your session.
Ardour knows about BWF files on import too, and will position imported BWF files in the correct position on the timeline.