Those patches usually do not download through your relays or BES Server. They download directly from Microsoft. If you look at the action, you will see both x86 and 64 bit are in the same action and you will see the action uses the Microsoft Update to download and install the updates, not a path to your server.
There are options to store the files on the local network and configure systems to update from there.
The download from Microsoft is a pain. If you have a baseline of office patches that all start at 8 PM, you could have dozens or even hundreds of systems downloading from Microsoft at the same time, causing network headaches.
The last thing that bothers me is the “Pause while”, basically waiting to see if the key changes to the new version because BigFix has no idea how far along the install is. It takes 20 min to determine the patch failed when it fails.
HCL has provided a lot of options around Office C2R versions, you just need to figure out what is best for you.