It is possible to do, but unless you are recording on film, it is probably much, much easier just to marker sync.
If your camera has an onboard mic, make sure it's on. If it doesn't, see if you can't get some mic on it (doesn't matter what it is - just has to capture audio). Then when you pull the footage in during post, match up the transients of your marker on each take. Just make sure you're in the same frame rate!!! (Logic should be set to record in 48k!)
If you don't have a way to get audio into the camera, you can still sync. Just line up the marker close frame with the transient of the audio. Using a frame bump quick key and scrub wheel, this should be a fairly quick process.
Then there is always the program "Plural Eyes" which pretty much does the above automatically (provided you have audio on the camera).
TC striping (as you described above - TV to audio track) really only works well if you have a clock you can send it back into. FCP only reads TC metadata, and unless you are going to re-record your tracks onto a machine with a TC input (DAT, XDCam, etc... or another computer with a TC input) it will just be too much of a headache on your part.
After all this is said, is there a reason you don't just record audio to the camera? It's not the best option in most situations, but this, being an interview, should really need much level riding, just boom movement (if even that). Then sync won't be an issue.