Reference existing media file

I am trying to "import" data including a file entity (pdf). I say import but I'm really just copying nodes from one content type to another, and perhaps there's a better way. But everything works well except for importing/referencing the uploaded files. I don't think I need to use the ::saveFile filter because the files are already in the database and on the server, but yet, I don't know what Feed Importer is expecting to receive.

If I DO use saveFile, will it "save" the file and not overwrite it, i.e. not add _0.pdf to the end?

Couldn't find any documentation on this... thanks for any help!