It’s also just not possible, as far as I know, to refer to site-attached files using Custom Site URLs in the same way as one would refer to the Uploads folder.
For instance, even knowing that my custom site “Test” on my root server has a URL of http://BES-Dev-Root:52311/cgi-bin/bfgather.exe/CustomSite_Test
, I still can’t navigate directly to a site file.
If I open that Gather URL in a browser, all I get is a reference to the current versions of the Site and the URLs to get to specific site versions:

Now, knowing that I have a few files attached to the site, I can observe that the files I attached without the ‘send to clients’ option, don’t appear in the site content at all.
I do have another file, “testfile.txt”, that I attached with the ‘send to clients’ option, and that one does appear in this list:

So, if I wanted, I expect I could set up a download command based on that URL. The /bfsites/CustomSite_Test_0_506/testfile.txt really does work…

But, it only works for as long as my Site Version 506 remains on the server. The root server only keeps a small number of site versions online - six versions by default, I think - so once I make seven more changes to my Test site, version 506 won’t be on the server anymore to download.
Nevermind that only the files I attached with the ‘Send to Clients’ option are even there and available the web server. And, if I attached those with the “send to clients” option, I don’t need to download it at all - it should already be there, on every client subscribed to the site. I can just read it directly from the client, no download needed:
q: lines of files "testfile.txt" of client folder of site "CustomSite_Test"
A: line 1
A: line 2
A: line 3