This is a bit technical answer based of my understanding PDF format , and experience with hand crafting my own PDF files.
PDF as a format is designed to be self contained. That is PDF lives under that assumption that you can craft a PDF file with your existing processes. The Predecessor of PDF, PostScript, however has these functions. PDF is in many ways just a programming facilities removed version of PostScript with a few additions on top. It is often much more conductive to do stuff in PostScript than in PDf if you need custom pipelines.
Technically however you can do this. Each PDF page is made out of streams, and each page could have multiple streams. So all you would need to do is override the logo stream and append this to the PDF file, then just override all the references to the next stream version and update the table of contents. IN practice you dont want to do this manually, unless your really into programming.
In practice you may still want to do this at the printer or with some external software. One such tool that could do this is GhostScript. But you could want to use some other pipelines too such as Apache FOP or even indesign on a server.
- Adobe. Document Management - Protable document format - part 1: PDF 1.7