1. The availability of a file is not the same as automatically loading it. The availability of the dotm from the network is strictly a Windows permission state.
If Word is there, there should be a Startup folder. You do not need to create it.
Word can indeed copy files, that is copy a file into Startup; it can also load template (macro) files from ANY folder. But template files in Startup are loaded at Startup, so if you run code FROM WORD to copy a file into Startup, that file will not load until the NEXT Startup.

So. One way would be to have the dotm in everyones Startup, and when a new user comes on board have part of the new user profile ensure that dotm is copied into that user's Startup.

What we did was have a wee tiny dotm copied into each user's Startup, and THAT one loaded a dotm from a network location. That way the REAL dotm was under control of the network, and everyone always loaded the latest. The file, being in one location (rather than multiple files in Startup) made for better management.