I would like to be able to embed a live web-hosted image into a PDF
file, so that when the PDF file is loaded up, it fetches the image
from the web.

Is there any way to do this with Adobe Acrobat, and if so - how? 

(The purpose of this is to create a 'web bug' to track readers of the
document in order to discover to what extent people are forwarding a
private copyrighted document without permission. I would be happy to
consider other methods of communicating between the PDF document and
the web server)