This is an interesting sceanario I have not seen personally implemented or attempted. I do not know much about the capabilities of hosting multimedia in a PDF. If the PDF could support a webpage in theory it could possibly support a Tableau Public viz using the embed link available in the share options. I think your best bet might be to have a static image of the Viz that can link out to either a Tableau Public or Tableau Online Viz for the user to view.
This would be an excellent idea to add to the Tableau Community Ideas forum!
Have you thought about doing it the other way, and sending out a Tableau Reader product which works kinda just like a .pdf ?