So, there are several ways you can approach this one. Here are just two. I'm sure others will chime in with additional methods.
1- Copy the PDF file in question to your Desktop, open Composer and drag/drop it into an empty spot on the left. It will create a new Source and pull in the doc with a path like /Users/yourHomeFolder/Desktop/FileName.pdf.
Create a DMG (not PKG), upload to your JSS, then be sure to check the Fill Existing Users checkbox (optionally the Fill User Template one too) once its in Casper Admin.
Deploy it via a policy as a Once per User trigger (again making sure to check the FEU and/or FUT boxes) and the JSS will drop the PDf file to everyone's Desktop when they log in.
2- Drop the PDF file into a common location on your admin Mac, like /Users/Shared/
Follow the same steps as above to capture your PDF in Composer. You can build it as either a PKG or DMG this time.
Add to your JSS, add in a policy to get it deployed to your Macs, and then use the Run Command option in the Advanced tab of the policy to do something like this:
ln -s /Users/Shared/FileName.pdf /Users/$(who | awk '/console/{ print $1 }')/Desktop/FileName
The above creates an alias of the file in /Users/Shared to the current logged in users Desktop.
As far as making sure it gets added again if someone deletes it, there are some ways you can accomplish this with an Extension Attribute, Smart Groups and ongoing policies but, I believe this may be a good use of something almost never used by anyone in Casper, which is the Self Healing function. Self Healing doesn't really work for applications, but it can sometimes work well for ensuring a document or link is always present. Read up on it in the full Casper Admin guide. The documentation is a little weak on how it works, but it should at least point you in the right direction.