IIUC what you say. No. Don't install a clean one and drop it, that will overwrite existing files and probably just screw up everything.
But what you say makes me think of an intermediate way: you can use the typical process to move a master to another machine, but then kind of "move it back".
Roughly:
1. Set up a server with Internet access
2. Stop the old server
3. Copy things from the existing one to the Internet ready one
4. Upgrade it following the standard docs
5. Move it back (rsync --delete)
Search the list about it. There's been plenty of discussions about it.
BTW makes me think we should create a page about that on
jenkins.io (if there is not already one)
HTH