I'm not an ADE expert or iRex user, but I think if your device is registered with ADE, you don't need to have ADE connected to the device to transfer the pdf.
You should be able to:
download the book thru ADE
exit ADE
start Calibre
load the PDF into calibre
transfer the book to the device using Calibre
This should work (I think); Calibre can be used to "manage" the book, it just can't modify or view the PDF.
Good luck, and I may be wrong.