I haven’t tried this myself as I don’t personally use FineReader, but if you do and you are interested in this Applescript that I came across today from UnderDoug.ca, check it out.
Remove Unprocessed By FineReader.scpt is a FolderAction AppleScript to remove files produced by ScanSnap like “/2008_12_28_17_32_30.pdf” once FineReader produces one like “2008_12_28_17_32_30 processed by FineReader.pdf”.
You can get the script here.