Yes, you need to download the document.

All I can offer is how I do it.  In fact, I just burned a couple pdf's to a CD then put in a different computer and printed them just to make sure it works.

I have a folder titled Downloads.  Everything I download goes into it.    Once you have it downloaded send it to to the CD burner.  It should work with no problem.  Burn it to a CD and take it to town.  Just remember, whoever prints it off for you will need to be able to open a pdf file.