I wouldn't say not possible, but definitely complex and a lot of work.
PDF files are a different format than a web page, so you would need to:
convert PDF -> HTML - maybe using Jave to go from PDF to XML-FO to HTML?
I have done <-> on my machine this way, so maybe you could do the conversions and FTP them to your site?
I have seen sites that let you read PDF files, but they load very slow. An indication of just how resource intensive the process is.
WordPress being PHP, you might think PHP's PDF functions. But AFAIK they only create PDFs not read them.
PHP does have ways to bridge to other languages (i.e. Java), but that's way over my head and I've never tried it.