Or maybe you may still use it locally, but you will have to manually copy/move it to somewhere else (basepath or homepath)?
Yes, this is the current plan.
You
also have to rename it, if you want to enable any executable code that it contains - but obtaining executable code from a random OpenArena server is a terrible idea security-wise. Even if the admin of the server you connected to happens to be trustworthy, there's nothing to stop malicious people from getting between you and the server, hijacking the connection and directing you to download their malware instead.
Please get all mods, but particularly the ones that intentionally contain executable code, from somewhere trustworthy.