I'm afraid I don't have that kind of information. All I know is from my own experience.
What I do know is that both Download Monitor and Email Before Download work perfectly when a full path is provided, including protocol and domain name. Download Monitor does not always work when protocol and domain name are omitted. This is because the given path is both used as a URL and as a file path. If you start this path with a / (because you want to be sure to start in the root folder), the URL part works fine, but the file path part does not. Because of the /, the system is trying to load the file from the root of the current drive. It's highly unlikely that your file can be found off the root of the current drive. The solution I use and that works for me, is omitting the starting /. I cannot guarantee this works for everyone though.
Even without the starting / in the path, Email Before Download does not work correctly. I found out that this is caused by the sending of the Location header. If I add the domain to the path, using the site_url function, it again works as expected.
BTW. The reason I don't use a full URL is that my site runs on several domains. I want each download to come from the referencing domain, not from one fixed domain.