No FCP OMF’s don’t transfer original timecodes or reel numbers. An EDL does. However, if the audio was imported as a file and not captured from a tape, then the EDL won’t have any timecode or reel information either.
The industry has a major problem with file based sources in all editing systems when it comes to transferring useful information to sound post. The good old EDL is becoming useless with non tape based sources. This is a huge issue when reversioning.
The rationale behind not transferring source timecode in an OMF is simple. AVID, who developed the OMF format, made it possible for the audio to be wav, aif or SD2. Only SD2 had the capacity to embed the source timecode, so basically the source code info was not transferred.
I am not sure but the Automatic Duck more transfer is likely to transfer the source code info.