If I am getting you correctly, you are wanting mobile PDFs to popup on a mobile screen.
If I wanted to do this I would consider the PDF first viewed on mobile… it would be an infinite pinch and zoom experience! If I really wanted this to work I would consider creating mobile versions of my PDFs for the mobile User.
I would then hide all desktop PDFs on the mobile device and introduce all my mobile version PDFs in a Sitely Popup way. I would stay away from html embedding!