Let the user add a PDF to a content type, but not as an attachment, content type is the pdf
This doesn't exactly answer your question (since maybe there is a module for that, but not that I'm aware), but here is what I do.

I have a content type for documents with two fields: summary/abstract and then a file upload field that accepts PDFs. If a PDF has a summary or abstract, I put the summary/abstract in that field and just link to the content's page figuring that the user can read that and then click on the document if they want. Otherwise, I still use this document content type to upload the file, leave the summary blank, and then link directly to the uploaded file itself. It would still have its own page created by the content type, but a site user isn't going to see that.