Yes and no. I would not trust that every document gets exported. Some may fail for one reason or another, and unless you keep careful track, you may delete documents that you shouldn't. So let's do this with a bit of panache.
1. In the source cabinet create a new numeric field and call it: ORIGDOCID.
2. In the source cabinet create a text field called OKTODELETE.
3. Run a SQL script on the source table to copy the DWDOCID to ORIGDOCID.
4. Create exactly the same field ORIGDOCID in the target cabinet.
5. Run the export workflow ensuring that you map ORIGDOCID to ORIGDOCID.
6. At the completion of the export you now have a reference from Target back to Source.
7. Create an Autoindex workflow, iterating the Target, and matching ORIGDOCID to DWDOCID in the Source.
8. Match first found document and update the OKTODELETE field in the source cabinet with "YES".
9. Create a deletion workflow that deletes document where OKTODELETE = "Yes".
Now you have control and won't lose any documents. You mave have to run the script in 3, for new documents periodically.