You might be one step ahead of google bots at this point in time since they primarily scan human readable text on web pages to assess duplicate content, but I highly would suggest not to make multiple copies of the same content as PDFs.
Also, publishing copies of the PDF does not necessarily mean more people will visit your site since they have other web sites they can access to download the PDF from.
Why not just write unique newsletters as HTML documents on your site and create a sitemap that lists the URL to each newsletter and submit it to google via webmaster tools?
Requiring a download of a PDF just to view text is sometimes a pain depending on your visitors.
Additionally, some users might not have a PDF reader installed. Some older phones that access the internet might not have sufficient technology to even install a PDF reader.