If you have a script that does the import you can add these steps
Set Variable: $$FileName Value://Your FileNameFieldhere
After the import is finished
Replace Field Contents Target Field: //Your FileNameFieldhere Specify Calculation: $$FileName
Make sure the found count stays the same while this happens, and it will only put the file name in the records you just imported.
Immediately after importing, the newly added records will form a "found set" of records. Replace Field Contents can then be used to assign a value to a field in every record in this found set.
This is a very powerful "batch update" tool that cannot be undone, so look it up in help before using and make a back up copy before you try it out just in case you don't get the results you expected.
Thanks guys for guiding me in this direction. I hope to get back to this problem and prototype something within the next few days and see what happens.
I appreciate the help!